scholarly journals J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of finite groups: maximal subgroups and ordinary characters for simple groups (Oxford University Press, 1985), xxxiii + 252 pp., £35.

1987 ◽  
Vol 30 (2) ◽  
pp. 325-325
Author(s):  
C. M. Campbell
Keyword(s):  
Finite Groups ◽  
Maximal Subgroups ◽  
Simple Groups ◽  
Oxford University ◽  
Oxford University Press

scholarly journals GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS

2020 ◽  
Vol 8 ◽  
Author(s):  
ANDREA LUCCHINI ◽  
CLAUDE MARION ◽  
GARETH TRACEY
Keyword(s):  
Finite Group ◽  
Maximal Subgroup ◽  
Simple Group ◽  
Finite Groups ◽  
Upper Bounds ◽  
Maximal Subgroups ◽  
Simple Groups ◽  
Almost Simple Group ◽  
Almost Simple Groups ◽  
A Finite Group

For a finite group $G$ , let $d(G)$ denote the minimal number of elements required to generate $G$ . In this paper, we prove sharp upper bounds on $d(H)$ whenever $H$ is a maximal subgroup of a finite almost simple group. In particular, we show that $d(H)\leqslant 5$ and that $d(H)\geqslant 4$ if and only if $H$ occurs in a known list. This improves a result of Burness, Liebeck and Shalev. The method involves the theory of crowns in finite groups.

Atlas of Finite Groups--Maximal Subgroups and Ordinary Characters for Simple Groups.

1987 ◽  
Vol 48 (177) ◽  
pp. 441 ◽  
Author(s):  
R. Steinberg ◽  
J. H. Conway ◽  
R. T. Curtis ◽  
S. P. Norton ◽  
R. A. Parker ◽  
...  
Keyword(s):  
Finite Groups ◽  
Maximal Subgroups ◽  
Simple Groups
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