c|Sections of Maximal Subgroups of Finite Groups

The subgroup structure of finite classical groups in terms of ... - AMiner

Maximal here means nothing more than maximal relative to inclusion. The general linear group, GLn(q), consists of the invertible linear transformations of an n- ...

Computing maximal subgroups of finite groups - WRAP: Warwick

We describe a practical algorithm for computing representatives of the conjugacy classes of maximal subgroups in a finite group, together with details of its ...

SUBGROUPS OF MAXIMAL RANK IN FINITE EXCEPTIONAL ...

The purpose of this paper is to investigate a large and natural class of maximal subgroups of the finite exceptional groups of Lie type, which we call subgroups ...

GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST ... - Unipd

... subgroups of wreath products appear as sections in finite groups. ... The latter is, in fact, a subgroup C of the Weyl group ... Scott, 'Maximal subgroups of finite ...

FINITE GROUPS WITH THREE CLASSES OF MAXIMAL ...

If such a group is not solvable, then its factor group modulo its Frattini subgroup is isomorphic to or , where is a prime. To prove this result, it was ...

Generating maximal subgroups of finite almost simple groups

Lucchini, A., Marion, C., & Tracey, G. (2020). Generating maximal subgroups of finite almost simple groups. Forum of Mathematics, Sigma, 8(e32). Lucchini ...

On -quasinormal and -normal subgroups of a finite group - EuDML

(2) if and only if there is a normal subgroup such that and every maximal subgroup of all Sylow subgroups of , the generalized Fitting subgroup of , is either - ...

On the Intersection of Certain Maximal Subgroups of a Finite Group

The next theorem provides a relationship between solvable PST-groups and. T2-groups. Theorem C. Let G be a group. If G= .G/ is a solvable PST-group, then G is a ...

Finite groups in which every maximal subgroup is nilpotent or ...

We prove that if every maximal subgroup of G G is nilpotent, or normal, or has p' p ′ -order, then (1) G G is solvable; (2) G G has a Sylow tower; (3) there ...

Bounds on the Number of Maximal Subgroups of Finite Groups - MDPI

In this paper, we obtain new bounds for the number of maximal subgroups of a given index in a finite group and we pin-point the universal ...

maximal subgroups of finite groups - UFDC Image Array 2

Every maximal subgroup of a finite solvable group has prime power index. Proof. See for example [5, Exercise 3B.1]. An important subgroup of a finite group ...

maximal Subgroups in Composite Finite Groups - CORE

* This set admits a natural permutation action by Inn S (if D E Inn S, iet it take c to the composite of 5 and inn ci); the orbits of this action match the ...

Finite Groups with Exactly Two Maximal Subgroups are Cyclic

Answering a viewer question, we prove that every finite group with exactly two maximal subgroups is cyclic. Along the way, we define maximal ...

Z-permutable subgroups on the structure of finite groups

(b) There is a normal subgroup H in G and a solvable normal subgroup C of F∗(H) such that G/H ∈ F, and the maximal subgroups of Gp ∩F∗(H) are C-Z-permutable.

Computing maximal subgroups of finite groups - CiteSeerX

the conjugacy classes of maximal subgroups C of N that neither avoid nor contain. S1. ... sections with S that are needed in the algorithm. ... Maximal subgroups of ...

A Characterization of Cyclic Groups via Indices of Maximal Subgroups

We prove the theorem in Sections 4 (finite groups) and 5 (infinite groups). In this section, we give two examples of groups that are not finitely generated, and ...

finite groups with all maximal subgroups

This completes the proof of the theorem except for the nilpotency of ~(G). which follows at once from 2. c. A number of theorems dealing with primitive solvable ...

Finite groups with solvable maximal subgroups - Typeset.io

that C(Af) is the intersection of all nilpotent maximal subgroups of. G. If a group G has a nilpotent maximal subgroup whose 2-Sylow subgroup is Abelian ...

On the maximal overgroups of Sylow subgroups of finite groups - arXiv

In this paper, we determine the finite groups with a Sylow r 𝑟 r italic_r -subgroup contained in a unique maximal subgroup. The proof involves ...

A survey of maximal subgroups of exceptional groups of Lie type

The first section deals with algebraic groups, and the second with finite groups. 1 Maximal subgroups of exceptional algebraic groups. Let G be a simple ...