Search results for "Group of Lie type"

A local approach to a class of locally finite groups

2003

This paper is devoted to the study of a class of generalised P-nilpotent groups in the universe cℒ̄ of all radical locally finite groups satisfying min-q for every prime q. Some results of finite groups are extended and a characterisation of the injectors associated with this class is given.

On the Quadratic Type of Some Simple Self-Dual Modules over Fields of Characteristic Two

1997

Let G be a finite group and let K be an algebraically closed field of Ž characteristic 2. Let V be a non-trivial simple self-dual KG-module we . say that V is self-dual if it is isomorphic to its dual V * . It is a theorem of w x Fong 4, Lemma 1 that in this case there is a non-degenerate G-invariant alternating bilinear form, F, say, defined on V = V. We say that V is a KG-module of quadratic type if F is the polarization of a non-degenerate w x G-invariant quadratic form defined on V. In a previous paper 6 , the present authors described some methods to decide if such a module V is of w x quadratic type. One of the main results of 6 is the following. Suppose that Ž . G is a group with a s…

Finite groups with subgroups supersoluble or subnormal

2009

Abstract The aim of this paper is to study the structure of finite groups whose non-subnormal subgroups lie in some subclasses of the class of finite supersoluble groups.

Complex group algebras of finite groups: Brauer’s Problem 1

2005

Brauer’s Problem 1 asks the following: what are the possible complex group algebras of finite groups? It seems that with the present knowledge of representation theory it is not possible to settle this question. The goal of this paper is to announce a partial solution to this problem. We conjecture that if the complex group algebra of a finite group does not have more than a fixed number m m of isomorphic summands, then its dimension is bounded in terms of m m . We prove that this is true for every finite group if it is true for the symmetric groups.

Some results concerning simple locally finite groups of 1-type

2005

AbstractIn this paper several aspects of infinite simple locally finite groups of 1-type are considered. In the first part, the classes of diagonal limits of finite alternating groups, of diagonal limits of finite direct products of alternating groups, and of absolutely simple groups of 1-type are distinguished from each other. In the second part, inductive systems of representations over fields of characteristic zero (which are known to correspond to ideals in the group algebra) are studied in general for groups of 1-type. The roles of primitive respectively imprimitive representations in inductive systems are investigated. Moreover it is shown that in any proper inductive system the depth…

A class of finite groups having nilpotent injectors

1986

AbstractThe purpose of this paper is to construct a class of groups which properly contains the class of N-constrained groups, and which is such that all groups in this class have N-injectors.

Automorphism groups of some affine and finite type Artin groups

2004

We observe that, for fixed n ≥ 3, each of the Artin groups of finite type An, Bn = Cn, and affine type ˜ An−1 and ˜ Cn−1 is a central extension of a finite index subgroup of the mapping class group of the (n + 2)-punctured sphere. (The centre is trivial in the affine case and infinite cyclic in the finite type cases). Using results of Ivanov and Korkmaz on abstract commensurators of surface mapping class groups we are able to determine the automorphism groups of each member of these four infinite families of Artin groups. A rank n Coxeter matrix is a symmetric n × n matrix M with integer entries mij ∈ N ∪ {∞} where mij ≥ 2 for ij, and mii = 1 for all 1 ≤ i ≤ n. Given any rank n Coxeter matr…

On a class of generalised Schmidt groups

2015

In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An A 5 -free group possessing one of these families is soluble, and soluble groups with this property have Fitting length at most three. A bound on the number of primes dividing the order of the group is also obtained.

Complex group algebras of finite groups: Brauer's Problem 1

2007

Abstract Brauer's Problem 1 asks the following: What are the possible complex group algebras of finite groups? It seems that with the present knowledge of representation theory it is not possible to settle this question. The goal of this paper is to present a partial solution to this problem. We conjecture that if the complex group algebra of a finite group does not have more than a fixed number m of isomorphic summands, then its dimension is bounded in terms of m . We prove that this is true for every finite group if it is true for the symmetric groups. The problem for symmetric groups reduces to an explicitly stated question in number theory or combinatorics.

On minimal subgroups of finite groups

1996