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.

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 the weakly monomial subgroups of finite simple groups

2019 ◽  
Vol 18 (02) ◽  
pp. 1950037
Author(s):  
Shuqin Dong ◽  
Hongfei Pan ◽  
Feng Tang
Keyword(s):  
Finite Group ◽  
Proper Subgroup ◽  
Maximal Subgroups ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Group A ◽  
A Finite Group

Let [Formula: see text] be a finite group. A proper subgroup [Formula: see text] of [Formula: see text] is said to be weakly monomial if the order of [Formula: see text] satisfies [Formula: see text]. In this paper, we determine all the weakly monomial maximal subgroups of finite simple groups.

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