Alessandro Montinaro

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On Flag‐Transitive Symmetric Designs of Affine Type

2016-09-20

Abstract It is shown that, if is a nontrivial 2‐ symmetric design, with , admitting a flag‐transitive automorphism group G of affine type, then , p an odd prime, and … Abstract It is shown that, if is a nontrivial 2‐ symmetric design, with , admitting a flag‐transitive automorphism group G of affine type, then , p an odd prime, and G is a point‐primitive, block‐primitive subgroup of . Moreover, acts flag‐transitively, point‐primitively on , and is isomorphic to the development of a difference set whose parameters and structure are also provided.

Nonsymmetric 2‐(v,k,λ) designs, with (r,λ) = 1, admitting a solvable flag‐transitive automorphism group of affine type

2019-09-24

Mauro Biliotti , Alessandro Montinaro , Pierluigi Rizzo

Abstract Nonsymmetric designs, with , admitting a solvable flag‐transitive automorphism group of affine type not contained in are classified. Abstract Nonsymmetric designs, with , admitting a solvable flag‐transitive automorphism group of affine type not contained in are classified.

Classification of the non-trivial 2-$$(v,k,\lambda )$$ designs, with $$ (r,\lambda )=1$$ and $$\lambda >1$$, admitting a non-solvable flag-transitive automorphism group of affine type

2021-11-17

Alessandro Montinaro , Mauro Biliotti , Eliana Francot

Block Designs with $$\gcd (r,\lambda )=1$$ Admitting Flag-Transitive Automorphism Groups

2022-06-21

Seyed Hassan Alavi , Mohsen Bayat , Mauro Biliotti +7 more

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2‐(v,k,1) Designs Admitting a Primitive Rank 3 Automorphism Group of Affine Type: The Extraspecial and the Exceptional Classes

2014-08-18

Alessandro Montinaro

Abstract 2‐( v,k,1 ) designs admitting a primitive rank 3 automorphism group , where G 0 belongs to the Extraspecial Class, or to the Exceptional Class of Liebeck's Theorem in … Abstract 2‐( v,k,1 ) designs admitting a primitive rank 3 automorphism group , where G 0 belongs to the Extraspecial Class, or to the Exceptional Class of Liebeck's Theorem in [23], are classified.

On flag‐transitive 2‐(k2,k,λ) $({k}^{2},k,\lambda )$ designs with λ∣k $\lambda | k$

2022-07-29

Alessandro Montinaro , Eliana Francot

Abstract It is shown that, apart from the smallest Ree group, a flag‐transitive automorphism group of a 2‐ design , with , is either an affine group or an almost … Abstract It is shown that, apart from the smallest Ree group, a flag‐transitive automorphism group of a 2‐ design , with , is either an affine group or an almost simple classical group. Moreover, when is the smallest Ree group, is isomorphic either to the 2‐ design or to one of the three 2‐ designs constructed in this paper. All the four 2‐designs have the 36 secants of a non‐degenerate conic of as a point set and 6‐sets of secants in a remarkable configuration as a block set.

The Doubly Transitive t-Parallelisms

2008-07-19

Norman L. Johnson , Alessandro Montinaro

2- $$(v,k,1)$$ ( v , k , 1 ) Designs with a point-primitive rank 3 automorphism group of affine type

2014-02-27

Mauro Biliotti , Alessandro Montinaro , Eliana Francot

Finite projective planes of order n with a 2-transitive orbit of length n – 3

2006-01-26

Mauro Biliotti , Alessandro Montinaro

Abstract We characterize the finite projective planes П of order n with a collineation group G acting 2-transitively on a point orbit of length n – 3. Aside from the … Abstract We characterize the finite projective planes П of order n with a collineation group G acting 2-transitively on a point orbit of length n – 3. Aside from the trivial cases, the plane П must have order 9 or 16 and G is isomorphic to PSL (2,5) or AGL (1,13), respectively.

The transitive t-parallelisms of a finite projective space

2012-06-01

Norman L. Johnson , Alessandro Montinaro

Classification of the non-trivial 2-(k2,k,λ) designs, with λ|k, admitting a flag-transitive almost simple automorphism group

2022-11-28

Alessandro Montinaro

Translation planes of order q 2 admitting a two-transitive orbit of length q + 1 on the line at infinity

2007-05-17

Mauro Biliotti , Vikram Jha , Norman L. Johnson +1 more

Large doubly transitive orbits on a line

2007-10-01

Alessandro Montinaro

Abstract Projective planes of order n with a coUineation group admitting a 2-transitive orbit on a line of length at least n /2 are investigated and new examples are provided. Abstract Projective planes of order n with a coUineation group admitting a 2-transitive orbit on a line of length at least n /2 are investigated and new examples are provided.

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A classification of flag-transitive 2-(k2,k,λ) designs with λ|k

2023-03-09

Alessandro Montinaro

Finite projective planes of order n with a 2 -transitive orbit of length n/2 - 1

2008-09-01

Alessandro Montinaro

On the Ree Unital

2007-12-12

Alessandro Montinaro

Classification of Projective Translation Planes of Order q2 Admitting a Two-Transitive Orbit of Length q + 1

2008-09-27

Mauro Biliotti , Vikram Jha , Norman L. Johnson +1 more

Coset switching in parallelisms

2008-02-14

Esteban Díaz Montenegro , Norman L. Johnson , Alessandro Montinaro

On the rigidity of the Figueroa replacement in PG(2, q 3)

2016-02-01

Mauro Biliotti , Alessandro Montinaro

The general structure of the projective planes admitting PSL(2,q) as a collineation group

2007-01-01

Alessandro Montinaro

Projective planes of order n admitting PSL(2, q), q > 3, as a collineation group are investigated for n ≤ q 2 .As a consequence, affine planes of order n … Projective planes of order n admitting PSL(2, q), q > 3, as a collineation group are investigated for n ≤ q 2 .As a consequence, affine planes of order n admitting PSL(2, q), q > 3, as a collineation group are classified for n < q 2 and (q, n) = (5, 16).Finally, a complete classification of the translation planes order n that admitting PSL(2, q), q > 3, as a collineation group is obtained for n ≤ q 2 .

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Projective Planes with a Doubly Transitive Projective Subplane

2007-03-01

Alessandro Montinaro

Projective planes of order up to q 3 with a collineation group G acting 2-transitively on a subplane of order q are investigated. Projective planes of order up to q 3 with a collineation group G acting 2-transitively on a subplane of order q are investigated.

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On the automorphism group of inversive planes of odd order

2012-01-16

Mauro Biliotti , Alessandro Montinaro

The Hall plane of order 9-revisited

2008-01-01

Mauro Biliotti , Vikram Jha , Norman L. Johnson +1 more

It is shown that the Hall plane of order 9 admits a collineation group isomorphic to SL(2,3) generated by Baer 3-collineations, whose Baer axes are disjoint as subspaces, where the … It is shown that the Hall plane of order 9 admits a collineation group isomorphic to SL(2,3) generated by Baer 3-collineations, whose Baer axes are disjoint as subspaces, where the union of whose components completely cover the components of the Hall plane. This group acts doubly transitive on a set of four points on the line at infinity of the plane.

A characterization of the desarguesian and the Figueroa planes of order $$q^{3}$$ q 3

2017-12-01

Mauro Biliotti , Alessandro Montinaro

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On the finite projective planes of order up to q4, q odd, admitting PSL(3,q) as a collineation group

2008-01-01

Mauro Biliotti , Alessandro Montinaro

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On the symmetric 2-(v,k,λ) designs with a flag-transitive point-imprimitive automorphism group

2024-05-08

Alessandro Montinaro

The symmetric 2-(v,k,λ) designs with k>λ(λ−3)/2 admitting a flag-transitive point-imprimitive automorphism group are completely classified: they are the known 2-designs with parameters (16,6,2),(45,12,3),(15,8,4) or (96,20,4). The symmetric 2-(v,k,λ) designs with k>λ(λ−3)/2 admitting a flag-transitive point-imprimitive automorphism group are completely classified: they are the known 2-designs with parameters (16,6,2),(45,12,3),(15,8,4) or (96,20,4).

Flag-transitive, point-imprimitive symmetric 2-(v,k,λ) designs with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>k</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">></mml:mo><mml:mi>λ</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mi>λ</mml:mi><mml:mo linebreak="badbreak" linebreakstyle="after">−</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn></mml:math>

2024-05-09

Alessandro Montinaro

Let D=(P,B) be a symmetric 2-(v,k,λ) design admitting a flag-transitive, point-imprimitive automorphism group G that leaves invariant a non-trivial partition Σ of P. Praeger and Zhou [42] have shown that, … Let D=(P,B) be a symmetric 2-(v,k,λ) design admitting a flag-transitive, point-imprimitive automorphism group G that leaves invariant a non-trivial partition Σ of P. Praeger and Zhou [42] have shown that, there is a constant k0 such that, for each B∈B and Δ∈Σ, the size of |B∩Δ| is either 0 or k0. In the present paper we show that, if k>λ(λ−3)/2 and k0⩾3, D is isomorphic to one of the known flag-transitive, point-imprimitive symmetric 2-designs with parameters (45,12,3) or (96,20,4).

On PGL (2, q )-invariant unitals embedded in Desarguesian or in Hughes planes

2013-06-20

Mauro Biliotti , Alessandro Montinaro

Affine planes admitting a collineation group with a transitive action on the line at infinity

2010-03-27

Mauro Biliotti , Alessandro Montinaro

Large 2-transitive arcs

2006-12-05

Alessandro Montinaro

Two-transitive groups on a hyperbolic unital

2007-09-08

Mauro Biliotti , Vikram Jha , Norman L. Johnson +1 more

A new characterization of the desarguesian and the Figueroa plane

2019-09-02

Eliana Francot , Alessandro Montinaro , Pierluigi Rizzo

A classification of the flag-transitive 2-(v,k,2) designs

2024-11-26

Hongxue Liang , Alessandro Montinaro

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Variations on a theme of Cofman

2010-10-20

Mauro Biliotti , Alessandro Montinaro

En The paper provides a survey on the known results on the collineation groups acting on a line of a projective plane with some transitivity properties. As a new result, … En The paper provides a survey on the known results on the collineation groups acting on a line of a projective plane with some transitivity properties. As a new result, it is shown that a group which is faithful and primitive of rank 3 on a line of a projective plane is 1-dimensional semilinear.

Transitive groups on the line at infinity of a finite affine plane

2010-10-28

Mauro Biliotti , Alessandro Montinaro

The Doubly-Transitive Focal-Spreads

2011-03-16

Norman L. Johnson , Alessandro Montinaro

An infinite class of 2-designs with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si27.gif" display="inline" overflow="scroll"><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>containing a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si28.gif" display="inline" overflow="scroll"><mml:mi>P</mml:mi><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:mrow></…

2013-06-06

Mauro Biliotti , Alessandro Montinaro

Flag-transitive and almost simple orbits in finite projective planes

2008-01-01

Alessandro Montinaro

Let Π be a projective plane of order n and let G be a collineation group of Π with a point-orbit O of length v.We investigate the triple (Π, O, … Let Π be a projective plane of order n and let G be a collineation group of Π with a point-orbit O of length v.We investigate the triple (Π, O, G) when O has the structure of a non trivial 2-(v, k, 1) design, G induces a flagtransitive and almost simple automorphism group on O and n ≤ P (O) = b + v + r + k.

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Flag-transitive, point-imprimitive symmetric $2$-$(v,k,λ)$ designs with $k>λ\left(λ-3 \right)/2$

2022-01-01

Alessandro Montinaro

Let $\mathcal{D}=\left(\mathcal{P},\mathcal{B} \right)$ be a symmetric $2$-$(v,k,\lambda )$ design admitting a flag-transitive, point-imprimitive automorphism group $G$ that leaves invariant a non-trivial partition $\Sigma$ of $\mathcal{P}$. Praeger and Zhou \cite{PZ} have … Let $\mathcal{D}=\left(\mathcal{P},\mathcal{B} \right)$ be a symmetric $2$-$(v,k,\lambda )$ design admitting a flag-transitive, point-imprimitive automorphism group $G$ that leaves invariant a non-trivial partition $\Sigma$ of $\mathcal{P}$. Praeger and Zhou \cite{PZ} have shown that, there is a constant $k_{0}$ such that, for each $B \in \mathcal{B}$ and $\Delta \in \Sigma$, the size of $\left\vert B \cap \Delta \right \vert$ is either $0$ or $k_{0}$. In the present paper we show that, if $k>\lambda \left(\lambda-3 \right)/2$ and $k_{0} \geq 3$, $\mathcal{D}$ is isomorphic to one of the known flag-transitive, point-imprimitive symmetric $2$-designs with parameters $(45,12,3)$ or $(96,20,4)$.

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On Flag-Transitive $2$-$(k^{2}, k, λ)$ Designs with $λ\mid k$

2022-01-01

Alessandro Montinaro , Eliana Francot

It is shown that, apart from the smallest Ree group, a flag-transitive automorphism group $G$ of a $2$-$(k^{2}, k, \lambda)$ design D, with $\lambda \mid k$, is either an affine … It is shown that, apart from the smallest Ree group, a flag-transitive automorphism group $G$ of a $2$-$(k^{2}, k, \lambda)$ design D, with $\lambda \mid k$, is either an affine group or an almost simple classical group. Moreover, when $G$ is the smallest Ree group, $\mathcal{D}$ is isomorphic either to the $2$-$(62, 6, 2)$ design or to one of the three $2$- $(62, 6, 6)$ designs constructed in this paper. All the four $2$-designs have the $36$ secants of a nondegenerate conic $\mathcal{C}$ of $PG_{2}(8)$ as a point set and 6-sets of secants in a remarkable configuration as a block set.

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Classification of the non-trivial $2$-$(k^{2},k,λ)$ designs, with $λ\mid k$, admitting a flag-transitive almost simple automorphism group

2022-01-01

Alessandro Montinaro

Non-trivial $2$-$(k^{2},k,\lambda )$ designs, with $\lambda \mid k$, admitting a flag-transitive almost simple automorphism group are classified. Non-trivial $2$-$(k^{2},k,\lambda )$ designs, with $\lambda \mid k$, admitting a flag-transitive almost simple automorphism group are classified.

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The transitive t-parallelisms of a finite projective space

2012-01-07

Norman L. Johnson , Alessandro Montinaro

Flag-transitive, point-imprimitive symmetric $2$-$(v,k,\lambda )$ designs with $k>\lambda \left(\lambda-3 \right)/2$

2022-03-17

Alessandro Montinaro

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Classification of the non-trivial $2$-$(k^{2},k,λ)$ designs, with $λ\mid k$, admitting a flag-transitive automorphism group of affine type

2022-01-01

Alessandro Montinaro

The pairs $(\mathcal{D},G)$, where $\mathcal{D}$ is a non-trivial $2$-$(k^{2},k,\lambda )$ design, with $\lambda \mid k$, and $G$ is a flag-transitive automorphism group of $\mathcal{D}$ of affine type such that $G … The pairs $(\mathcal{D},G)$, where $\mathcal{D}$ is a non-trivial $2$-$(k^{2},k,\lambda )$ design, with $\lambda \mid k$, and $G$ is a flag-transitive automorphism group of $\mathcal{D}$ of affine type such that $G \nleq A \Gamma L_{1}(k^{2})$, are classified.

Block designs with $\gcd(r,λ)=1$ admitting flag-transitive automorphism groups

2022-01-01

Seyed Hassan Alavi , Mohsen Bayat , Mauro Biliotti +7 more

In this paper, we present a classification of $2$-designs with $\gcd(r,\lambda)=1$ admitting flag-transitive automorphism groups. If $G$ is a flag-transitive automorphism group of a non-trivial $2$-design $\mathcal{D}$ with $\gcd(r,\lambda)=1$, then … In this paper, we present a classification of $2$-designs with $\gcd(r,\lambda)=1$ admitting flag-transitive automorphism groups. If $G$ is a flag-transitive automorphism group of a non-trivial $2$-design $\mathcal{D}$ with $\gcd(r,\lambda)=1$, then either $(\mathcal{D},G)$ is one of the known examples described in this paper, or $\mathcal{D}$ has $q = p^{d}$ points with $p$ prime and $G$ is a subgroup of $A\Gamma L_{1}(q)$.

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Flag-transitive symmetric $2$-designs]{The symmetric $2$-$(v,k,λ)$ designs, with $k>λ\left(λ-3 \right)/2$, admitting a flag-transitive, point imprimitive automorphism group are known

2022-01-01

Alessandro Montinaro

The symmetric $2$-$(v,k,\lambda )$ designs, with $k>\lambda \left(\lambda-3 \right)/2$, admitting a flag-transitive, point-imprimitive automorphism group are completely classified: they are the known $2$-designs with parameters $(16,6,2),(45,12,3),(15,8,4)$ or $(96,20,4)$. The symmetric $2$-$(v,k,\lambda )$ designs, with $k>\lambda \left(\lambda-3 \right)/2$, admitting a flag-transitive, point-imprimitive automorphism group are completely classified: they are the known $2$-designs with parameters $(16,6,2),(45,12,3),(15,8,4)$ or $(96,20,4)$.

On quasi-Hermitian varieties in even characteristic and related orthogonal arrays

2023-01-01

Angela Aguglia , Luca Giuzzi , Alessandro Montinaro +1 more

In this paper we study the BM quasi-Hermitian varieties introduced in [A. Aguglia, A. Cossidente, G. Korchm\`aros, On quasi-Hermitian Varieties, J. Combin. Des. 20 (2012) 433-447.] in characteristc $2$ and … In this paper we study the BM quasi-Hermitian varieties introduced in [A. Aguglia, A. Cossidente, G. Korchm\`aros, On quasi-Hermitian Varieties, J. Combin. Des. 20 (2012) 433-447.] in characteristc $2$ and dimension $3$. After a brief investigation of their combinatorial properties, we first show that all of these varieties are projectively equivalent in non-zero even characteristic, exhibiting a behavior which is strikingly different from what happens in odd characteristic, see [A. Aguglia, L. Giuzzi, On the equivalence of certain quasi-Hermitian varieties, J. Combin. Des. 1-15 (2022)]. This completes the classification project started in that paper. Next, by using previous results, we explicitly determine and investigate the structure of the full collineation group stabilizing these varieties. Finally, as a byproduct of our investigation, we also construct and a family of simple orthogonal arrays $OA(q^5,q^4,q,2)$ with entries in ${\mathbb F}_q$ where $q$ is a power of $2$.

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A Classification of the flag-transitive $2$-$(v,k,2)$ designs

2024-04-02

Hongxue Liang , Alessandro Montinaro

In this paper, we provide a complete classification of $2$-$(v,k,2)$ design admitting a flag-transitive automorphism group of affine type with the only exception of the semilinear $1$-dimensional group. Alongside this … In this paper, we provide a complete classification of $2$-$(v,k,2)$ design admitting a flag-transitive automorphism group of affine type with the only exception of the semilinear $1$-dimensional group. Alongside this analysis we provide a construction of seven new families of such flag-transitive $2$-designs, two of them infinite, and some of them involve remarkable objects such as $t$-spreads, translation planes, quadrics and Segre varieties. Our result together with those Alavi et al. [1,2], Praeger et al. [15], Zhou and the first author [37,38] provides a complete classification of $2$-$(v,k,2)$ design admitting a flag-transitive automorphism group with the only exception of the semilinear $1$-dimensional case.

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A Classification of the flag-transitive $2$-$(v,3,\lambda)$ designs with with $v\equiv 1,3\pmod{6}$ and $v \equiv 6 \pmod{\lambda}$

2024-04-03

Eliana Francot , Alessandro Montinaro

In this paper, we provide a complete classification of the $2$-$(v,3,\lambda )$ designs with $v\equiv 1,3\pmod{6}$ and $% v \equiv 6 \pmod{\lambda}$ admitting a flag-transitive automorphism group non-isomorphic to a … In this paper, we provide a complete classification of the $2$-$(v,3,\lambda )$ designs with $v\equiv 1,3\pmod{6}$ and $% v \equiv 6 \pmod{\lambda}$ admitting a flag-transitive automorphism group non-isomorphic to a subgroup of $A\Gamma L_{1}(v)$.

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Analysing 2-$(v,k,2)$ designs admitting a flag-transitive almost simple automorphism group with socle $PSL(2,q)$ by means of conics and hyperovals of $PG(2,q)$

2024-04-29

Alessandro Montinaro , Yanwei Zhao , Zhilin Zhang +1 more

The classification of the $2$-designs with $\lambda=2$ admitting a flag-transitive automorphism groups with socle $PSL(2,q)$ is completed by settling the two open cases in \cite{ABDT}. The result is achieved by … The classification of the $2$-designs with $\lambda=2$ admitting a flag-transitive automorphism groups with socle $PSL(2,q)$ is completed by settling the two open cases in \cite{ABDT}. The result is achieved by using conics and hyperovals of $PG(2,q)$.

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Affine groups as flag-transitive and point-primitive automorphism groups of symmetric designs

2025-05-02

Seyed Hassan Alavi , Mohsen Bayat , Ashraf Daneshkhah +1 more

A Classification of the Flag‐Transitive 2‐(v,3,λ) $(v,3,\lambda )$ Designs With v≡1,3(mod6) $v\equiv 1,3\,(\mathrm{mod}\,6)$ and v≡6(modλ) $v\equiv 6\,(\mathrm{mod}\,\lambda )$

2025-03-05

Alessandro Montinaro , Eliana Francot

ABSTRACT In this paper, we provide a complete classification of the 2‐ designs with and admitting a flag‐transitive automorphism group non‐isomorphic to a subgroup of . ABSTRACT In this paper, we provide a complete classification of the 2‐ designs with and admitting a flag‐transitive automorphism group non‐isomorphic to a subgroup of .

On Quasi‐Hermitian Varieties in Even Characteristic and Related Orthogonal Arrays

2025-01-06

Angela Aguglia , Luca Giuzzi , Alessandro Montinaro +1 more

ABSTRACT In this article, we study the BM quasi‐Hermitian varieties, laying in the three‐dimensional Desarguesian projective space of even order. After a brief investigation of their combinatorial properties, we first … ABSTRACT In this article, we study the BM quasi‐Hermitian varieties, laying in the three‐dimensional Desarguesian projective space of even order. After a brief investigation of their combinatorial properties, we first show that all of these varieties are projectively equivalent, exhibiting a behavior which is strikingly different from what happens in odd characteristic. This completes the classification project started there. Here we prove more; indeed, by using previous results, we explicitly determine the structure of the full collineation group stabilizing these varieties. Finally, as a byproduct of our investigation, we also construct a family of simple orthogonal arrays , with entries in , where is an even prime power. Orthogonal arrays (OA's) are principally used to minimize the number of experiments needed to investigate how variables in testing interact with each other.

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A classification of the flag-transitive 2-(v,k,2) designs

2024-11-26

Hongxue Liang , Alessandro Montinaro

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Affine groups as flag-transitive and point-primitive automorphism groups of symmetric designs

2024-09-07

Seyed Hassan Alavi , Mohsen Bayat , Ashraf Daneshkhah +1 more

In this article, we investigate symmetric designs admitting a flag-transitive and point-primitive affine automorphism group. We prove that if an automorphism group $G$ of a symmetric $(v,k,\lambda)$ design with $\lambda$ … In this article, we investigate symmetric designs admitting a flag-transitive and point-primitive affine automorphism group. We prove that if an automorphism group $G$ of a symmetric $(v,k,\lambda)$ design with $\lambda$ prime is point-primitive of affine type, then $G=2^{6}{:}\mathrm{S}_{6}$ and $(v,k,\lambda)=(16,6,2)$, or $G$ is a subgroup of $\mathrm{A\Gamma L}_{1}(q)$ for some odd prime power $q$. In conclusion, we present a classification of flag-transitive and point-primitive symmetric designs with $\lambda$ prime, which says that such an incidence structure is a projective space $\mathrm{PG}(n,q)$, it has parameter set $(15,7,3)$, $(7, 4, 2)$, $(11, 5, 2)$, $(11, 6, 2)$, $(16,6,2)$ or $(45, 12, 3)$, or $v=p^d$ where $p$ is an odd prime and the automorphism group is a subgroup of $\mathrm{A\Gamma L}_{1}(q)$.

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Designs with a simple automorphism group

2024-08-09

Alessandro Montinaro , Yanwei Zhao , Zhilin Zhang +1 more

Flag-transitive, point-imprimitive symmetric 2-(v,k,λ) designs with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>k</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">></mml:mo><mml:mi>λ</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mi>λ</mml:mi><mml:mo linebreak="badbreak" linebreakstyle="after">−</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn></mml:math>

2024-05-09

Alessandro Montinaro

On the symmetric 2-(v,k,λ) designs with a flag-transitive point-imprimitive automorphism group

2024-05-08

Alessandro Montinaro

Analysing 2-$(v,k,2)$ designs admitting a flag-transitive almost simple automorphism group with socle $PSL(2,q)$ by means of conics and hyperovals of $PG(2,q)$

2024-04-29

Alessandro Montinaro , Yanwei Zhao , Zhilin Zhang +1 more

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A Classification of the flag-transitive $2$-$(v,3,\lambda)$ designs with with $v\equiv 1,3\pmod{6}$ and $v \equiv 6 \pmod{\lambda}$

2024-04-03

Eliana Francot , Alessandro Montinaro

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A Classification of the flag-transitive $2$-$(v,k,2)$ designs

2024-04-02

Hongxue Liang , Alessandro Montinaro

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A classification of flag-transitive 2-(k2,k,λ) designs with λ|k

2023-03-09

Alessandro Montinaro

On quasi-Hermitian varieties in even characteristic and related orthogonal arrays

2023-01-01

Angela Aguglia , Luca Giuzzi , Alessandro Montinaro +1 more

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Classification of the non-trivial 2-(k2,k,λ) designs, with λ|k, admitting a flag-transitive almost simple automorphism group

2022-11-28

Alessandro Montinaro

On flag‐transitive 2‐(k2,k,λ) $({k}^{2},k,\lambda )$ designs with λ∣k $\lambda | k$

2022-07-29

Alessandro Montinaro , Eliana Francot

Block Designs with $$\gcd (r,\lambda )=1$$ Admitting Flag-Transitive Automorphism Groups

2022-06-21

Seyed Hassan Alavi , Mohsen Bayat , Mauro Biliotti +7 more

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Flag-transitive, point-imprimitive symmetric $2$-$(v,k,\lambda )$ designs with $k>\lambda \left(\lambda-3 \right)/2$

2022-03-17

Alessandro Montinaro

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Flag-transitive, point-imprimitive symmetric $2$-$(v,k,λ)$ designs with $k>λ\left(λ-3 \right)/2$

2022-01-01

Alessandro Montinaro

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On Flag-Transitive $2$-$(k^{2}, k, λ)$ Designs with $λ\mid k$

2022-01-01

Alessandro Montinaro , Eliana Francot

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Classification of the non-trivial $2$-$(k^{2},k,λ)$ designs, with $λ\mid k$, admitting a flag-transitive almost simple automorphism group

2022-01-01

Alessandro Montinaro

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Classification of the non-trivial $2$-$(k^{2},k,λ)$ designs, with $λ\mid k$, admitting a flag-transitive automorphism group of affine type

2022-01-01

Alessandro Montinaro

Block designs with $\gcd(r,λ)=1$ admitting flag-transitive automorphism groups

2022-01-01

Seyed Hassan Alavi , Mohsen Bayat , Mauro Biliotti +7 more

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Flag-transitive symmetric $2$-designs]{The symmetric $2$-$(v,k,λ)$ designs, with $k>λ\left(λ-3 \right)/2$, admitting a flag-transitive, point imprimitive automorphism group are known

2022-01-01

Alessandro Montinaro

Classification of the non-trivial 2-$$(v,k,\lambda )$$ designs, with $$ (r,\lambda )=1$$ and $$\lambda >1$$, admitting a non-solvable flag-transitive automorphism group of affine type

2021-11-17

Alessandro Montinaro , Mauro Biliotti , Eliana Francot

Nonsymmetric 2‐(v,k,λ) designs, with (r,λ) = 1, admitting a solvable flag‐transitive automorphism group of affine type

2019-09-24

Mauro Biliotti , Alessandro Montinaro , Pierluigi Rizzo

A new characterization of the desarguesian and the Figueroa plane

2019-09-02

Eliana Francot , Alessandro Montinaro , Pierluigi Rizzo

A characterization of the desarguesian and the Figueroa planes of order $$q^{3}$$ q 3

2017-12-01

Mauro Biliotti , Alessandro Montinaro

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On Flag‐Transitive Symmetric Designs of Affine Type

2016-09-20

Mauro Biliotti , Alessandro Montinaro

On the rigidity of the Figueroa replacement in PG(2, q 3)

2016-02-01

Mauro Biliotti , Alessandro Montinaro

2‐(v,k,1) Designs Admitting a Primitive Rank 3 Automorphism Group of Affine Type: The Extraspecial and the Exceptional Classes

2014-08-18

Alessandro Montinaro

2- $$(v,k,1)$$ ( v , k , 1 ) Designs with a point-primitive rank 3 automorphism group of affine type

2014-02-27

Mauro Biliotti , Alessandro Montinaro , Eliana Francot

On PGL (2, q )-invariant unitals embedded in Desarguesian or in Hughes planes

2013-06-20

Mauro Biliotti , Alessandro Montinaro

An infinite class of 2-designs with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si27.gif" display="inline" overflow="scroll"><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>containing a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si28.gif" display="inline" overflow="scroll"><mml:mi>P</mml:mi><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:mrow></…

2013-06-06

Mauro Biliotti , Alessandro Montinaro

The transitive t-parallelisms of a finite projective space

2012-06-01

Norman L. Johnson , Alessandro Montinaro

On the automorphism group of inversive planes of odd order

2012-01-16

Mauro Biliotti , Alessandro Montinaro

The transitive t-parallelisms of a finite projective space

2012-01-07

Norman L. Johnson , Alessandro Montinaro

The Doubly-Transitive Focal-Spreads

2011-03-16

Norman L. Johnson , Alessandro Montinaro

Transitive groups on the line at infinity of a finite affine plane

2010-10-28

Mauro Biliotti , Alessandro Montinaro

Variations on a theme of Cofman

2010-10-20

Mauro Biliotti , Alessandro Montinaro

Affine planes admitting a collineation group with a transitive action on the line at infinity

2010-03-27

Mauro Biliotti , Alessandro Montinaro

Classification of Projective Translation Planes of Order q2 Admitting a Two-Transitive Orbit of Length q + 1

2008-09-27

Mauro Biliotti , Vikram Jha , Norman L. Johnson +1 more

Finite projective planes of order n with a 2 -transitive orbit of length n/2 - 1

2008-09-01

Alessandro Montinaro

The Doubly Transitive t-Parallelisms

2008-07-19

Norman L. Johnson , Alessandro Montinaro

Coset switching in parallelisms

2008-02-14

Esteban Díaz Montenegro , Norman L. Johnson , Alessandro Montinaro

The Hall plane of order 9-revisited

2008-01-01

Mauro Biliotti , Vikram Jha , Norman L. Johnson +1 more

Flag-transitive and almost simple orbits in finite projective planes

2008-01-01

Alessandro Montinaro

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On the finite projective planes of order up to q4, q odd, admitting PSL(3,q) as a collineation group

2008-01-01

Mauro Biliotti , Alessandro Montinaro

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On the Ree Unital

2007-12-12

Alessandro Montinaro

Large doubly transitive orbits on a line

2007-10-01

Alessandro Montinaro

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Two-transitive groups on a hyperbolic unital

2007-09-08

Mauro Biliotti , Vikram Jha , Norman L. Johnson +1 more

Coauthor	Papers Together
Mauro Biliotti	20
Eliana Francot	9
Norman L. Johnson	8
Vikram Jha	4
Mohsen Bayat	4
Seyed Hassan Alavi	4
Ashraf Daneshkhah	4
Shenglin Zhou	3
Pierluigi Rizzo	2
Xiaoqin Zhan	2
Zhilin Zhang	2
Haiyan Guan	2
Yanwei Zhao	2
Hongxue Liang	2
Delu Tian	2
Viola Siconolfi	2
Luca Giuzzi	2
Pierluigi Rizzo	2
Angela Aguglia	2
Fatemeh Mouseli	2
Yongli Zhang	2
Yajie Wang	2
Norman L. Johnson	1
Yan Zhu	1
Shenglin Zhou	1
Esteban Díaz Montenegro	1
Yan Zhu	1

Homogeneous designs and geometric lattices

1985-01-01

William M. Kantor

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The Classification of Finite Linear Spaces with Flag-Transitive Automorphism Groups of Affine Type

1998-11-01

Martin W. Liebeck

Atlas of Finite Groups--Maximal Subgroups and Ordinary Characters for Simple Groups.

1987-01-01

R. Steinberg , J. H. Conway , Robert T. Curtis +3 more

This atlas covers groups from the families of the classification of finite simple groups. Recently updated incorporating corrections This atlas covers groups from the families of the classification of finite simple groups. Recently updated incorporating corrections

Two-transitive orbits in finite projective planes

2005-08-01

Mauro Biliotti , Eliana Francot

Transitive linear groups and linear groups which contain irreducible subgroups of prime order

1974-02-01

Christoph Hering

The Affine Permutation Groups of Rank Three

1987-05-01

Martin W. Liebeck

On Finite Linear Spaces with Almost Simple Flag-Transitive Automorphism Groups

2002-11-01

Jan Saxl

Determination of the Ternary Collineation Groups Whose Coefficients Lie in the GF(2 n )

1925-12-01

Richard Hartley

Linear spaces with flag-transitive automophism groups

1990-10-01

Francis Buekenhout , Anne Delandtsheer , Jean Doyen +3 more

PSL(2,q) as a collineation group of projective planes of small order

1989-07-01

G. Eric Moorhouse

On a Class of Doubly Transitive Groups

1962-01-01

Michio Suzuki

Involutory collineations of finite planes

1986-06-01

Chat Yin Ho

On Flag‐Transitive Symmetric Designs of Affine Type

2016-09-20

Mauro Biliotti , Alessandro Montinaro

Flag-transitivity and primitivity

1987-01-01

Huw M. L. Davies

On a Class of Doubly Transitive Groups: II

1964-05-01

Michio Suzuki

Abstract : This study considers a class of doubly transitive groups satisfying the condition that the identity is the only element leaving three distinct letters fixed. The main object of … Abstract : This study considers a class of doubly transitive groups satisfying the condition that the identity is the only element leaving three distinct letters fixed. The main object of the investigation is to classify the groups which do not contain a regular normal subgroup of order 1 + N in case N is even. (Author)

Solvable primitive permutation groups of low rank

1969-01-01

David A. Foulser

On primitivity and reduction for flag-transitive symmetric designs

2004-12-15

Eugenia O’Reilly-Regueiro

On the structure of finite collineation groups of projective planes

1979-05-01

Christoph Hering

Flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1 and alternating socle

2015-05-27

Yan Zhu , Haiyan Guan , Shenglin Zhou

On flag-transitive 2-(v,k,2) designs

2020-08-24

Alice Devillers , Hongxue Liang , Cheryl E. Praeger +1 more

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Solvable flag transitive affine groups

1964-01-01

David A. Foulser

Flag transitive automorphism groups of 2-designs with (γ, λ) = 1

1988-11-01

Paul-Hermann Zieschang

Non-symmetric 2-designs admitting a two-dimensional projective linear group

2018-03-21

Xiaoqin Zhan , Shenglin Zhou

Linear Groups with an Exposition of the Galois Field Theory

1959-10-01

L. E. Dickson , J. Gillis

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The rank 3 permutation representations of the finite classical groups

1982-01-01

William M. Kantor , Robert A. Liebler

The permutation representations in the title are all determined, and no surprises are found to occur. The permutation representations in the title are all determined, and no surprises are found to occur.

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Nonsymmetric 2‐(v,k,λ) designs, with (r,λ) = 1, admitting a solvable flag‐transitive automorphism group of affine type

2019-09-24

Mauro Biliotti , Alessandro Montinaro , Pierluigi Rizzo

Perspectivities in irreducible collineation groups of projective planes, II

1979-01-01

Christoph Hering , Michael J. Walker

Overgroups of Cyclic Sylow Subgroups of Linear Groups

2008-06-04

John Bamberg , Tim Penttila

Abstract We use a theorem of Guralnick, Penttila, Praeger, and Saxl to classify the subgroups of the general linear group (of a finite dimensional vector space over a finite field) … Abstract We use a theorem of Guralnick, Penttila, Praeger, and Saxl to classify the subgroups of the general linear group (of a finite dimensional vector space over a finite field) which are overgroups of a cyclic Sylow subgroup. In particular, our results provide the starting point for the classification of transitive m-systems; which include the transitive ovoids and spreads of finite polar spaces. We also use our results to prove a conjecture of Cameron and Liebler on irreducible collineation groups having equally many orbits on points and on lines. Key Words: Cameron–Liebler conjecture m-systemMatrix groupOvoidPrimitive prime divisorSpread2000 Mathematics Subject Classification: Primary 20G40Secondary 20C20, 20C33, 20C34 ACKNOWLEDGMENT We would like to thank Michael Giudici for many fruitful and stimulating conversations. This work forms part of an Australian Research Council Discovery Grant, for which the first author was supported. Notes Communicated by D. Easdown. Additional informationNotes on contributorsJohn Bamberg* *Current affiliation: Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000 Ghent, Belgium. Tim Penttila** **Current affiliation: Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA; E-mail: [email protected]

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Some remarks concerning the Ree groups of type (G2)

1966-03-01

Heinz Lüneburg

On the maximal subgroups of the finite classical groups

1984-10-01

Michael Aschbacher

Flag-transitive non-symmetric 2-designs with $$(r,\lambda )=1$$ ( r , λ ) = 1 and sporadic socle

2016-01-06

Xiaoqin Zhan , Shenglin Zhou

Determination of the ordinary and modular ternary linear groups

1911-01-01

Howard H. Mitchell

Throughout the paper; denotes the modulus.The discussion of the binary groups applies also to the casep = 2. * This type of Diophantine equation originated in C. Jordan's attempt to … Throughout the paper; denotes the modulus.The discussion of the binary groups applies also to the casep = 2. * This type of Diophantine equation originated in C. Jordan's attempt to determine all finite collineation groups in the ordinary plane, Journal für die reine und angewandte

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Classification of the non-trivial 2-$$(v,k,\lambda )$$ designs, with $$ (r,\lambda )=1$$ and $$\lambda >1$$, admitting a non-solvable flag-transitive automorphism group of affine type

2021-11-17

Alessandro Montinaro , Mauro Biliotti , Eliana Francot

Finite exceptional groups of Lie type and symmetric designs

2022-03-31

Seyed Hassan Alavi , Mohsen Bayat , Ashraf Daneshkhah

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The maximal subgroups of the chevalley groups G2(q) with q odd, the Ree groups 2G2(q), and their automorphism groups

1988-08-01

Peter B. Kleidman

Collineation groups doubly transitive on the points at infinity in an affine plane of order (2 r )

1981-12-01

G. Korchm�ros

Flag-Transitive Subgroups of Chevalley Groups

1973-01-01

Gary M. Seitz

Publisher Summary Let G be a finite group of Chevalley type and B the Borel subgroup of G. If L ≤ G and G = BL, then L is said … Publisher Summary Let G be a finite group of Chevalley type and B the Borel subgroup of G. If L ≤ G and G = BL, then L is said to be flagtransitive. D. Higman determined all flag-transitive subgroups of G in case G is of type A n . This chapter presents an extension of Higman's theorem to the case of a general group of Chevalley type. The result is used to show the nonexistence of 2-transitive permutation representations of certain groups of Chevalley type.

The full collineation group of any projective plane of order 12 is a {2, 3}-group

1982-01-01

Zvonimir Janko , Tran van Trung

On Unitary Polarities of Finite Projective Planes

1971-12-01

William M. Kantor

A unitary polarity of a finite projective plane of order q 2 is a polarity θ having q 3 + 1 absolute points and such that each nonabsolute line contains … A unitary polarity of a finite projective plane of order q 2 is a polarity θ having q 3 + 1 absolute points and such that each nonabsolute line contains precisely q + 1 absolute points. Let G ( θ ) be the group of collineations of centralizing θ . In [ 15 ] and [ 16 ], A. Hoffer considered restrictions on G ( θ ) which force to be desarguesian. The present paper is a continuation of Hoffer's work. The following are our main results. THEOREM I. Let θ be a unitary polarity of a finite projective plane of order q 2 . Suppose that Γ is a subgroup of G ( θ ) transitive on the pairs x, X, with x an absolute point and X a nonabsolute line containing x. Then is desarguesian and Γ contains PSU(3, q ).

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