On a conjecture of G.E. Wall

Martin W. Liebeck, Laszlo Pyber, Aner Shalev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

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 C r- 2 / 3 | G |, 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 2 C | G |3 / 2 maximal subgroups.

Original languageAmerican English
Pages (from-to)184-197
Number of pages14
JournalJournal of Algebra
Volume317
Issue number1
DOIs
StatePublished - 1 Nov 2007

Bibliographical note

Funding Information:
✩ The second author was supported by grants OTKA T049841 and NK62321. The third author acknowledges the support of an EPSRC Visiting Fellowship. * Corresponding author. E-mail address: shalev@math.huji.ac.il (A. Shalev).

Keywords

  • Finite groups
  • Finite simple groups
  • Maximal subgroups

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