On a conjecture of GE wall

[摘要] We prove that if G is a finite almost simple group, having socle of Lie type of rank r, then the number of maximal subgroups of G is at most Cr-2/3 vertical bar G vertical bar, where C is an absolute constant. This verifies a conjecture of Wall for groups of sufficiently large rank. Using this we prove that any finite group G has at most 2C vertical bar G vertical bar(3/2) maximal subgroups. (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-01

[关键词] maximal subgroups;finite groups;finite simple groups