Our object is to describe all of the-primitive permutation groups of degree less than 1000 together with some of their significant properties. We think that such a list is of …
Our object is to describe all of the-primitive permutation groups of degree less than 1000 together with some of their significant properties. We think that such a list is of interest in illustrating in concrete form the kinds of primitive groups which arise, in suggesting conjectures about primitive groups, and in settling small exceptional cases which often occur in proofs of theorems about permutation groups. The range that we consider is large enough to allow examples of most of the types of primitive group to appear. Earlier lists (of varying completeness and accuracy) of primitive groups of degree d have been published by: C. Jordan (1872) [21] for d ≤ 17, by W. Burnside (1897) [5] for d ≤ 8, by Manning (1929) [34–38] for d ≤ 15, by C. C. Sims (1970) [45] for d ≤ 20, and by B. A. Pogorelev (1980) [42] for d ≤ 50. Unpublished lists have also been prepared by C. C. Sims for d ≤ 50 and by Mizutani[41] for d ≤ 48. Using the classification of finite simple groups which was completed in 1981 we have been able to extend the list much further. Our task has been greatly simplified by the detailed information about many finite simple groups which is available in the Atlas of Finite Groups which we will refer to as the Atlas [8].
This is a personal account of an attempt, and failure, to popularize mathematics in the undergraduate community of a university. We hope to convince you that this was an exciting …
This is a personal account of an attempt, and failure, to popularize mathematics in the undergraduate community of a university. We hope to convince you that this was an exciting adventure, with much scope and promise, and to warn you of the political problems that arose and finally aborted the project. The idea was to offer a mathematics enrichment course for students who had completed freshman mathematics but were pursuing careers in other disciplines. Two particular target groups were in mind: the first consisted of students and alumni we meet occasionally who are still enthusiastic about mathematics. Although they never went beyond freshman mathematics they can still wax nostalgic about their former romance with mathematics. They want to know more about mathematics. The second was a more nebulous group, students who might be destined for positions of influence for funding mathematics at the national level, and therefore presumably would obtain university degrees and see something of mathematics along the way.
Let p be a rational prime and n a positive integer ≥2. We denote by a n (p) the least positive integral value of a for which the polynomial x …
Let p be a rational prime and n a positive integer ≥2. We denote by a n (p) the least positive integral value of a for which the polynomial x n +x+a is irreducible (mod p ), and set (1)
This is a personal account of an attempt, and failure, to popularize mathematics in the undergraduate community of a university. We hope to convince you that this was an exciting …
This is a personal account of an attempt, and failure, to popularize mathematics in the undergraduate community of a university. We hope to convince you that this was an exciting adventure, with much scope and promise, and to warn you of the political problems that arose and finally aborted the project. The idea was to offer a mathematics enrichment course for students who had completed freshman mathematics but were pursuing careers in other disciplines. Two particular target groups were in mind: the first consisted of students and alumni we meet occasionally who are still enthusiastic about mathematics. Although they never went beyond freshman mathematics they can still wax nostalgic about their former romance with mathematics. They want to know more about mathematics. The second was a more nebulous group, students who might be destined for positions of influence for funding mathematics at the national level, and therefore presumably would obtain university degrees and see something of mathematics along the way.
Our object is to describe all of the-primitive permutation groups of degree less than 1000 together with some of their significant properties. We think that such a list is of …
Our object is to describe all of the-primitive permutation groups of degree less than 1000 together with some of their significant properties. We think that such a list is of interest in illustrating in concrete form the kinds of primitive groups which arise, in suggesting conjectures about primitive groups, and in settling small exceptional cases which often occur in proofs of theorems about permutation groups. The range that we consider is large enough to allow examples of most of the types of primitive group to appear. Earlier lists (of varying completeness and accuracy) of primitive groups of degree d have been published by: C. Jordan (1872) [21] for d ≤ 17, by W. Burnside (1897) [5] for d ≤ 8, by Manning (1929) [34–38] for d ≤ 15, by C. C. Sims (1970) [45] for d ≤ 20, and by B. A. Pogorelev (1980) [42] for d ≤ 50. Unpublished lists have also been prepared by C. C. Sims for d ≤ 50 and by Mizutani[41] for d ≤ 48. Using the classification of finite simple groups which was completed in 1981 we have been able to extend the list much further. Our task has been greatly simplified by the detailed information about many finite simple groups which is available in the Atlas of Finite Groups which we will refer to as the Atlas [8].
Let p be a rational prime and n a positive integer ≥2. We denote by a n (p) the least positive integral value of a for which the polynomial x …
Let p be a rational prime and n a positive integer ≥2. We denote by a n (p) the least positive integral value of a for which the polynomial x n +x+a is irreducible (mod p ), and set (1)
Abstract We give a self-contained proof of the O'Nan-Scott Theorem for finite primitive permutation groups.
Abstract We give a self-contained proof of the O'Nan-Scott Theorem for finite primitive permutation groups.
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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MICHAEL ASCHBACHER Let G be a doubly transitive permutation group on a set of degree n 2 mod 4, n > 2. Let a and B be distinguished and distinct …
MICHAEL ASCHBACHER Let G be a doubly transitive permutation group on a set of degree n 2 mod 4, n > 2. Let a and B be distinguished and distinct points in ,
It is proved that if G is a permutation group on a set Ω every orbit of which contains more than mn elements, then any pair of subsets of Ω …
It is proved that if G is a permutation group on a set Ω every orbit of which contains more than mn elements, then any pair of subsets of Ω containing m and n elements respectively can be separated by an element of G .
Introduction and definitions. Let S be a set of points. By an nsubset of S we shall mean a subset of S consisting of precisely n points. Let S be …
Introduction and definitions. Let S be a set of points. By an nsubset of S we shall mean a subset of S consisting of precisely n points. Let S be a subset of S and G a group of 1-1 transformations of S upon itself. Then G is weakly n-transitive over S if for any two n-subsets Xi, X2 of S there exists a gGG such that g(Xl) = X2. (It is not required that g(S) CS.) In particular if S= S, S is a topological space, and G is the group of homeomorphisms of S upon itself, then the space S is said to be weakly n-homogeneous.1 The purpose of this paper is to prove that an infinite weakly nhomogeneous topological space is weakly (n 1)-homogeneous (n> 1).