Maximal subgroups of finite simple groups and their automorphism groups

1992 ◽  
pp. 243-259 ◽  
Author(s):  
Martin W. Liebeck ◽  
Jan Saxl
Keyword(s):  
Automorphism Groups ◽  
Maximal Subgroups ◽  
Simple Groups ◽  
Finite Simple Groups

On conjugacy classes of maximal subgroups of finite simple groups, and a related zeta function

2005 ◽  
Vol 128 (3) ◽  
pp. 541-557 ◽  
Author(s):  
Martin W. Liebeck ◽  
Benjamin M. S. Martin ◽  
Aner Shalev
Keyword(s):  
Zeta Function ◽  
Conjugacy Classes ◽  
Maximal Subgroups ◽  
Simple Groups ◽  
Finite Simple Groups

scholarly journals On the maximal subgroups of finite simple groups

1964 ◽  
Vol 1 (2) ◽  
pp. 168-213 ◽  
Author(s):  
Daniel Gorenstein ◽  
John H Walter
Keyword(s):  
Maximal Subgroups ◽  
Simple Groups ◽  
Finite Simple Groups

scholarly journals Finite simple groups with nilpotent third maximal subgroups

1966 ◽  
Vol 6 (4) ◽  
pp. 466-469 ◽  
Author(s):  
T. M. Gagen ◽  
Z. Janko
Keyword(s):  
Maximal Subgroup ◽  
Maximal Subgroups ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
A Chain

We say that a subgroup H is an n-th maximal subgroup of G if there exists a chain of subgroups G = G0 > G1 > … > Gn = H such that each Gi is a maximal subgroup of Gi-1, i = 1, 2, …, n. The purpose of this note is to classify all finite simple groups with the property that every third maximal subgroup is nilpotent.

scholarly journals A new construction of the Ree groups of type 2G2

2010 ◽  
Vol 53 (2) ◽  
pp. 531-542 ◽  
Author(s):  
Robert A. Wilson
Keyword(s):  
Lie Algebras ◽  
Algebraic Groups ◽  
Maximal Subgroups ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
New Construction ◽  
Elementary Construction

AbstractWe give a new elementary construction of Ree's family of finite simple groups of type 2G2, which avoids the need for the machinery of Lie algebras and algebraic groups. We prove that the groups we construct are simple of order q3(q3 + 1)(q − 1) and act doubly transitively on an explicit set of q3 + 1 points, where q = 32k+1. Moreover, our construction is practical in the sense that generators for the groups and many of their maximal subgroups may easily be obtained.

scholarly journals A note on the automorphism groups of cubic Cayley graphs of finite simple groups

2010 ◽  
Vol 310 (21) ◽  
pp. 3030-3032 ◽  
Author(s):  
Cui Zhang ◽  
Xin Gui Fang
Keyword(s):  
Automorphism Groups ◽  
Cayley Graphs ◽  
Simple Groups ◽  
Finite Simple Groups

On the centers of maximal subgroups of locally finite simple groups of alternating type

2002 ◽  
Vol 5 (4) ◽  
Author(s):  
Neil Flowers ◽  
Ulrich Meierfrankenfeld
Keyword(s):  
Maximal Subgroups ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Locally Finite

Finite simple groups with complemented maximal subgroups

2006 ◽  
Vol 47 (4) ◽  
pp. 659-668 ◽  
Author(s):  
V. M. Levchuk ◽  
A. G. Likharev
Keyword(s):  
Maximal Subgroups ◽  
Simple Groups ◽  
Finite Simple Groups

On Automorphism Groups of Symmetric Cayley Graphs of Finite Simple Groups with Valency Six

2010 ◽  
Vol 17 (01) ◽  
pp. 161-172
Author(s):  
Xingui Fang ◽  
Pu Niu ◽  
Jie Wang
Keyword(s):  
Automorphism Groups ◽  
Cayley Graphs ◽  
Simple Groups ◽  
Finite Simple Groups

In this paper we investigate the full automorphism groups of six-valent symmetric Cayley graphs Γ = Cay (G,S) for finite non-abelian simple groups G. We prove that for most finite non-abelian simple groups G, if Γ contains no cycle of length 4, then Aut Γ = G · Aut (G,S), where Aut (G,S) ≤ S 6.

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