Helmut Wielandt

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Helmut Wielandt (December 19, 1910 – February 14, 2001) was a German mathematician known primarily for his influential work in group theory. He made pioneering contributions to the study of subnormal subgroups and other structural aspects of finite groups. Wielandt served as a professor at several German universities, including the University of Tübingen, and authored important texts on finite groups and permutation groups. His work left a lasting impact on modern algebra.

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Finite Permutation Groups.

1966-08-01

Franklin Haimo , Helmut Wielandt

Unzerlegbare, nicht negative Matrizen

1950-12-01

Helmut Wielandt

Zur Theorie der einfach transitiven Permutationsgruppen

1936-12-01

Helmut Wielandt

An extremum property of sums of eigenvalues

1955-01-01

Helmut Wielandt

We present in this note a maximum-minimum characterization of sums like a3+a7+asj where a1> . * * a. are the eigenvalues of a hermitian nXn matrix. The result contains the … We present in this note a maximum-minimum characterization of sums like a3+a7+asj where a1> . * * a. are the eigenvalues of a hermitian nXn matrix. The result contains the classic characterization of am as well as the maximum property of a1+a2+ * * * +a. given recently by Fan [4]. Though the result is valid also for a completely continuous hermitian operator in Hilbert space, we shall for the sake of simplicity assume the dimension to be finite. As an application we obtain linear inequalities relating the eigenvalues of the sum of two hermitian matrices to the eigenvalues of the summands.

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Zum Satz von Sylow

1954-12-01

Helmut Wielandt

Über Produkte von nilpotenten Gruppen

1958-12-02

Helmut Wielandt

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On eigenvalues of sums of normal matrices

1955-12-01

Helmut Wielandt

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Beziehungen zwischen den Fixpunktzahlen von Automorphismengruppen einer endlichen Gruppe

1960-04-01

Helmut Wielandt

Zur Theorie der einfach transitiven Permutationsgruppen. II

1950-12-01

Helmut Wielandt

�ber das Produkt paarweise vertauschbarer nilpotenter Gruppen

1951-02-01

Helmut Wielandt

Kriterien f�r Subnormalit�t in endlichen Gruppen

1974-10-01

Helmut Wielandt

An Extremum Property of Sums of Eigenvalues

1955-02-01

Helmut Wielandt

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Primitive Permutationsgruppen vom Grad 2p

1955-12-01

Helmut Wielandt

Über die Existenz von Normalteilern in endlichen Gruppen

1958-01-01

Helmut Wielandt

Error bounds for eigenvalues of symmetric integral equations [28]

1996-12-31

Helmut Wielandt

Error bounds for eigenvalues of symmetric integral equations

1956-01-01

Helmut Wielandt

Ein Beweis f�r die Existenz der Sylowgruppen

1959-12-01

Helmut Wielandt

Über die Eigenwertaufgaben mit reellen diskreten Eigenwerten. Erhard Schmidt zum 75. Geburtstag gewidmet

1950-01-01

Helmut Wielandt

Zum Satz von Sylow. II

1959-12-01

Helmut Wielandt

Endlichek-homogene Permutationsgruppen

1967-01-01

Helmut Wielandt

�ber das Erzeugnis paarweise kosubnormaler Untergruppen

1980-12-01

Helmut Wielandt

Über die Normalstruktur von mehrfach faktorisierten Gruppen

1960-02-01

Helmut Wielandt

Ein Teil von Philip Halls bekannter Theorie der auflösbaren Gruppen läßt sich, wie im folgenden gezeigt wird, auf beliebige endiliche Gruppen G ausdehnen. Wir fragen: Was kann man über die … Ein Teil von Philip Halls bekannter Theorie der auflösbaren Gruppen läßt sich, wie im folgenden gezeigt wird, auf beliebige endiliche Gruppen G ausdehnen. Wir fragen: Was kann man über die Normalstruktur (Hauptreihen, Kompositionsfaktoren) von G aussagen, wenn man mehrere Zer legungen von G in Produkte von Untergruppen mit gegebener Normalstruktur kennt? Eine Antwort gibt der folgende Satz, das Hauptergebnis dieser Note:

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Linear relations between higher additive commutators

1962-10-01

Olga Taussky , Helmut Wielandt

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Nested bounds for the Perron root of a nonnegative matrix

1983-07-01

Emeric Deutsch , Helmut Wielandt

Normalteiler mehrfach transitiver Permutationsgruppen

1958-04-01

Helmut Wielandt , Bertram Huppert

�ber den Transitivit�tsgrad von Permutationsgruppen

1960-12-01

Helmut Wielandt

Pairs of normal matrices with property L

1953-08-01

Helmut Wielandt

A short proof is given , under weaker ass ump tions, of t he foll owi ng theore m firs t proverl by K. Wiegman n: If t he e … A short proof is given , under weaker ass ump tions, of t he foll owi ng theore m firs t proverl by K. Wiegman n: If t he e igenvalu es a i, /3i of t wo normal n X n matrices A, B may be nUIllbered in s uch a wa .vthat t he eigen values I' i(Z) of C ( z )= a +zb are given by I'i(Z) = I' i+ Z/3 i (fo r i =

Subnormale H�llen in Permutationsgruppen

1962-12-01

Helmut Wielandt

Multiply Transitive Groups

1964-01-01

Helmut Wielandt

Normalteiler in 3-transitiven Gruppen

1974-09-01

Helmut Wielandt

p-Sylowgruppen und p-Faktorgruppen [6]

2012-03-24

Helmut Wielandt , Bertram Huppert , Hans Schneider

Zur Abgrenzung der selbstadjungierten Eigenwertaufgaben. I. Räume endlicher Dimension

1949-01-01

Helmut Wielandt

Error bounds for eigenvalues of Hermitian integral equations and infinite matrices [23]

1996-12-31

Helmut Wielandt

The Method of Schur

1964-01-01

Helmut Wielandt

Fundamental Concepts

1964-01-01

Helmut Wielandt

Linear relations between higher additive commutators (with Olga Taussiy) [50]

1996-12-31

Helmut Wielandt

Nested bounds for the Perron root of a nonnegative matrix (with Emeric Deutsch) [69]

1996-12-31

Helmut Wielandt

On the role of the determinant in semigroups of matrices (with Olga Taussky) [52]

1996-12-31

Helmut Wielandt

The Transitive Constituents of Gα

1964-01-01

Helmut Wielandt

p-Sylowgruppen und p-Faktorgruppen [6]

2012-03-24

Helmut Wielandt , Bertram Huppert , Hans Schneider

Error bounds for eigenvalues of symmetric integral equations [28]

1996-12-31

Helmut Wielandt

Linear relations between higher additive commutators (with Olga Taussiy) [50]

1996-12-31

Helmut Wielandt

Error bounds for eigenvalues of Hermitian integral equations and infinite matrices [23]

1996-12-31

Helmut Wielandt

Nested bounds for the Perron root of a nonnegative matrix (with Emeric Deutsch) [69]

1996-12-31

Helmut Wielandt

On the role of the determinant in semigroups of matrices (with Olga Taussky) [52]

1996-12-31

Helmut Wielandt

Nested bounds for the Perron root of a nonnegative matrix

1983-07-01

Emeric Deutsch , Helmut Wielandt

�ber das Erzeugnis paarweise kosubnormaler Untergruppen

1980-12-01

Helmut Wielandt

Kriterien f�r Subnormalit�t in endlichen Gruppen

1974-10-01

Helmut Wielandt

Normalteiler in 3-transitiven Gruppen

1974-09-01

Helmut Wielandt

Endlichek-homogene Permutationsgruppen

1967-01-01

Helmut Wielandt

Finite Permutation Groups.

1966-08-01

Franklin Haimo , Helmut Wielandt

Multiply Transitive Groups

1964-01-01

Helmut Wielandt

The Method of Schur

1964-01-01

Helmut Wielandt

Fundamental Concepts

1964-01-01

Helmut Wielandt

The Transitive Constituents of Gα

1964-01-01

Helmut Wielandt

Subnormale H�llen in Permutationsgruppen

1962-12-01

Helmut Wielandt

Linear relations between higher additive commutators

1962-10-01

Olga Taussky , Helmut Wielandt

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�ber den Transitivit�tsgrad von Permutationsgruppen

1960-12-01

Helmut Wielandt

Beziehungen zwischen den Fixpunktzahlen von Automorphismengruppen einer endlichen Gruppe

1960-04-01

Helmut Wielandt

Über die Normalstruktur von mehrfach faktorisierten Gruppen

1960-02-01

Helmut Wielandt

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Ein Beweis f�r die Existenz der Sylowgruppen

1959-12-01

Helmut Wielandt

Zum Satz von Sylow. II

1959-12-01

Helmut Wielandt

Über Produkte von nilpotenten Gruppen

1958-12-02

Helmut Wielandt

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Normalteiler mehrfach transitiver Permutationsgruppen

1958-04-01

Helmut Wielandt , Bertram Huppert

Über die Existenz von Normalteilern in endlichen Gruppen

1958-01-01

Helmut Wielandt

Error bounds for eigenvalues of symmetric integral equations

1956-01-01

Helmut Wielandt

Primitive Permutationsgruppen vom Grad 2p

1955-12-01

Helmut Wielandt

On eigenvalues of sums of normal matrices

1955-12-01

Helmut Wielandt

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An Extremum Property of Sums of Eigenvalues

1955-02-01

Helmut Wielandt

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An extremum property of sums of eigenvalues

1955-01-01

Helmut Wielandt

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Zum Satz von Sylow

1954-12-01

Helmut Wielandt

Pairs of normal matrices with property L

1953-08-01

Helmut Wielandt

�ber das Produkt paarweise vertauschbarer nilpotenter Gruppen

1951-02-01

Helmut Wielandt

Unzerlegbare, nicht negative Matrizen

1950-12-01

Helmut Wielandt

Zur Theorie der einfach transitiven Permutationsgruppen. II

1950-12-01

Helmut Wielandt

Über die Eigenwertaufgaben mit reellen diskreten Eigenwerten. Erhard Schmidt zum 75. Geburtstag gewidmet

1950-01-01

Helmut Wielandt

Zur Abgrenzung der selbstadjungierten Eigenwertaufgaben. I. Räume endlicher Dimension

1949-01-01

Helmut Wielandt

Zur Theorie der einfach transitiven Permutationsgruppen

1936-12-01

Helmut Wielandt

Coauthor	Papers Together
Olga Taussky	1
Franklin Haimo	1
Bertram Huppert	1
Emeric Deutsch	1
Bertram Huppert	1
Hans Schneider	1

A Characteristic Property of Soluble Groups

1937-07-01

P. Hall

On some Properties of Groups of Odd Order

1900-11-01

W. Burnside

is any set of characteristics, and Xp Xj* •••» Xr a set for which \\ is unity, then XiXi» X2X2' • " ' X r X r is a set … is any set of characteristics, and Xp Xj* •••» Xr a set for which \\ is unity, then XiXi» X2X2' • " ' X r X r is a set of characteristics.Returning to the irreducible representation of the group in the form «,' -"?* n e £x* (x* +1) homogeneous products of the second degree of the x's are transformed lineai'ly among themselves by every operation of the group; and, for this representation, the sum of the multipliers of any operation is equal to the sum of the homogeneous products two together of the multipliers in the above irreducible form.Hence, by similar reasoning to that employed above, there must be positive integers e,-,, such thatwhere 4*1 ia the sum of the homogeneous products two together of the multipliers whose sum is xi-In this way it may be shown that, if any symmetric function be formed of x' symbols, a system of equations of the form (ii), in which the e's are positive integers, must hold when i/^ is the symmetric function formed.from, the multipliers whose sum is xi-In particular, the products of the multipliers for each set of conjugate operations in any representation of the group constitutes a set of characteristics for which \i 18 unity.On some Properties of Groins of Odd Order.By W. BURNSIDE.

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Zur Theorie der einfach transitiven Permutationsgruppen

1936-12-01

Helmut Wielandt

On a Theorem of Weyl Concerning Eigenvalues of Linear Transformations I

1949-11-01

Ky Fan

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Theorems Like Sylow's

1956-04-01

Philip Hall

Einschlie�ungssatz f�r die charakteristischen Zahlen von Matrizen

1942-12-01

L. Collatz

On the Sylow Systems of a Soluble Group<sup>†</sup>

1938-01-01

Philip Hall

A Note on Soluble Groups

1928-04-01

Philip Hall

Focal Series in Finite Groups

1953-01-01

D. G. Higman

If there is given a subgroup 5 of a (finite) group G, we may ask what information is to be obtained about the structure of G from a knowledge of … If there is given a subgroup 5 of a (finite) group G, we may ask what information is to be obtained about the structure of G from a knowledge of the location of S in G. Thus, for example, famed theorems of Frobenius and Burnside give criteria for the existence of a normal subgroup N of G such that G = NS and 1 = N ⋂ S, and hence in particular for the non-simplicity of G. To aid in locating S in G, and to facilitate exploitation of the transfer, we single out a descending chain of normal subgroups of S. Namely, we introduce the focal series of S in G by means of the recursive formulae

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Sur quelques applications des fonctions convexes et concaves au sens de I. Schur

1984-01-01

Alexander Ostrowski

Théorèmes sur les groupes primitifs.

1871-01-01

Camille Jordan

On the Sylow Systems of a Soluble Group

1938-01-01

P. Hall

Theory of Groups of Finite Order

1911-12-01

G. B. M.

On eigenvalues of sums of normal matrices [27]

1996-12-31

Robert C. Thompson

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On the change of index for summable series

1955-12-01

Dieter Gaier

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�ber das Produkt paarweise vertauschbarer nilpotenter Gruppen

1951-02-01

Helmut Wielandt

Remarks on splitting extensions

1954-12-01

D. G. Higman

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Sur la limite de transitivité des groupes non alternés

1872-01-01

Camille Jordan

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Sur les racines d'une équation fondamentale

1902-01-01

Ivar Bendixson

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Die Automorphismon der projektiven Gruppen

1928-12-01

Otto Schreier , B. L. Van der WAERDEN

On infinite groups

1955-12-01

W. R. Scott

COROLLARY 2. // i(H)=B 9 then G has a normal subgroup K such that <B B .Proof.Let N(H) denote the normalizer of H, and Cί(H) the conjugate class of H. … COROLLARY 2. // i(H)=B 9 then G has a normal subgroup K such that <B B .Proof.Let N(H) denote the normalizer of H, and Cί(H) the conjugate class of H. Then

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Bounds for the Perron root of a nonnegative irreducible partitioned matrix

1981-01-01

Emeric Deutsch

It is well-known that the Perron root of a nonnegative irreducible matrix lies between the smallest and the largest row sum of A. This result is generalized to the case … It is well-known that the Perron root of a nonnegative irreducible matrix lies between the smallest and the largest row sum of A. This result is generalized to the case when the matrix A is partitioned into blocks.

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Contributions to the theory of groups of finite order

1939-06-01

Öystein Ore

Equiangular lines, the Graph Extension Theorem, and transfer in triply transitive groups

1974-06-01

Mark Hale , Ernest E. Shult

On the Factorization of Finite Groups

1974-02-01

A. D. Sands

Finite Permutation Groups.

1966-08-01

Franklin Haimo , Helmut Wielandt

Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements

1957-07-01

Graham Higman

Üeber die Struktur der endlichen Gruppen, deren echte Untergruppen sämtlich nilpotent sind

1941-01-01

Kenkiti Iwasawa

Derivations in Simple Rings

1957-01-01

S. A. Amitsur

An inequality for sets of integers

1955-12-01

Peter Scherk

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Kriterien f�r Subnormalit�t in endlichen Gruppen

1974-10-01

Helmut Wielandt

On homogeneous linear differential equations with arbitrary constant coefficients

1955-12-01

A. Seidenberg

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Zweifach transitive, aufl�sbare Permutationsgruppen

1957-12-01

Bertram Huppert

Zur Theorie der Matrices

1907-06-01

Oskar Perron

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A criterion for the permutability of subnormal subgroups

1975-07-01

D.C Brewster

The measure ring for a cube of arbitrary dimension

1955-12-01

J. M. G. Fell

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Sugli automorfismi privi di coincidenze nei gruppi finiti.

1957-01-01

Guido Zappa

Minimal basis and inessential discriminant divisors for a cubic field

1955-12-01

Leonard Tornheim

In terms of the coefficients OC, jS, γ of a defining equation of a cubic field F over the rational number field Q 9 Albert [l] has given an explicit … In terms of the coefficients OC, jS, γ of a defining equation of a cubic field F over the rational number field Q 9 Albert [l] has given an explicit formula for a minimal basis, that is, a basis of the integers of Q{θ) over the rational integers.We solve this same problem with a shorter proof and a simpler result.This basis is then used to find the maximal inessential discriminant divisor, that is, the square root of the quotient of the g.c.d. of the discriminants of all integers of Q(θ) by the discriminant of Q(θ).It is known[3] that the only prime dividing it is 2; we determine the power as 2° or 2 ι .We first secure a normalized generating quantity, LEMMA 1.If K is any cubic field, then K = Q(θ) with (2) 6> 3 + aθ 2 + 6 = 0, where (i) a and b are rational integers, (ii) no factor of a has its cube dividing b 9 and (iii) if 3 \\a, then the discriminant Δ =b (4α 3 + 27 b) of θ is not divisible by 3 4 unless 3 | b.Here g n |1 y means g n | γ and g n l \γ.Proof.The substitution θ'~ θ+ α/3 is used to obtain an equation of form(1) with α zero.Follow this by the substitution 0'= 1/0 to obtain (2).For Conditions (i) and (ii) it is obvious that a substitution 0'= hθ will be effective.If (iii) does not hold apply the substitution 0'= ab -3 bθ + a 2 θ 2 ; then 0' 3 + cθ' 2 +d = 0 where

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On a conjecture of Frobenius

1956-01-01

Walter Feit

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Traite des substitutions et des equations algebriques

1870-01-01

Marie Ennemond Camille Jordan

On Primitive Groups of Odd Order

1904-01-01

H. L. Rietz

A Search for Analogues of the Mathieu Group

1958-01-01

E. T. Parker , Paul J. Nikolai

On quadruply transitive groups

1959-09-01

E. T. Parker

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Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung)

1912-12-01

Hermann Weyl

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Cantor-type uniqueness of multiple trigonometric integrals

1955-12-01

Victor L. Shapiro

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Zum Satz von Sylow

1954-12-01

Helmut Wielandt

Primitive, auflösbare Permutationsgruppen

1955-05-01

Bertram Huppert

Estimate for the Perron Root of a Nonnegative Matrix

2008-01-01

LU Hong-bin

We studied the bounds of Perron root of a nonnegative matrix, and defined the 1-path cover of directed graph. With the help of the directed graph and 1-path cover of … We studied the bounds of Perron root of a nonnegative matrix, and defined the 1-path cover of directed graph. With the help of the directed graph and 1-path cover of directed graph, we gave a new method to estimate the super bounds and lower bounds of Perron root of a nonnegative matrix, and obtained some new results.

On the homomorphisms of an algebra onto Frobenius algebras

1955-12-01

W. E. Deskins

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Methoden der mathematischen Physik

1993-01-01

Richard Courant , David Hilbert