On a conjecture of G.E. Wall

Martin W. Liebeck; Laszlo Pyber; Aner Shalev

doi:10.1016/j.jalgebra.2006.10.047

On a conjecture of G.E. Wall

Martin W. Liebeck
, Laszlo Pyber
, Aner Shalev^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

27 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 language	English
Pages (from-to)	184-197
Number of pages	14
Journal	Journal of Algebra
Volume	317
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2006.10.047
State	Published - 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: [email protected] (A. Shalev).

Keywords

Finite groups
Finite simple groups
Maximal subgroups

Access to Document

10.1016/j.jalgebra.2006.10.047

Cite this

@article{b37be2f9889f4bdf8784ea7d8c0e1959,

title = "On a conjecture of G.E. Wall",

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.",

keywords = "Finite groups, Finite simple groups, Maximal subgroups",

author = "Liebeck, \{Martin W.\} and Laszlo Pyber and Aner Shalev",

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: [email protected] (A. Shalev).",

year = "2007",

month = nov,

day = "1",

doi = "10.1016/j.jalgebra.2006.10.047",

language = "אנגלית",

volume = "317",

pages = "184--197",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - On a conjecture of G.E. Wall

AU - Liebeck, Martin W.

AU - Pyber, Laszlo

AU - Shalev, Aner

N1 - 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: [email protected] (A. Shalev).

PY - 2007/11/1

Y1 - 2007/11/1

N2 - 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.

AB - 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.

KW - Finite groups

KW - Finite simple groups

KW - Maximal subgroups

UR - https://www.scopus.com/pages/publications/34548772340

U2 - 10.1016/j.jalgebra.2006.10.047

DO - 10.1016/j.jalgebra.2006.10.047

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:34548772340

SN - 0021-8693

VL - 317

SP - 184

EP - 197

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

On a conjecture of G.E. Wall

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this