On the generation of simple groups by Sylow subgroups

Tim  Burness; Robert Guralnick

doi:10.1090/conm/800/16051

On the generation of simple groups by Sylow subgroups

Tim Burness
, Robert Guralnick

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

1 Citation (Scopus)

190 Downloads (Pure)

Abstract

Let G be a finite simple group of Lie type and let P be a Sylow 2-subgroup of G. In this paper, we prove that for any nontrivial element x ∈ G, there exists g ∈ G such that G = hP, xg i. By combining this result with recent work of Breuer and Guralnick, we deduce that if G is a finite nonabelian simple group and r is any prime divisor of |G|, then G is generated by a Sylow 2-subgroup and a Sylow r-subgroup

Original language	English
Title of host publication	Amitsur Centennial Symposium
Editors	Avinoam Mann, Louis H. Rowen, David J. Saltman, Aner Shalev, Lance W. Small, Uzi Vishne
Publisher	American Mathematical Society
Chapter	4
Pages	81-100
Number of pages	20
ISBN (Electronic)	9781470476137
ISBN (Print)	9781470475550
DOIs	https://doi.org/10.1090/conm/800/16051
Publication status	Published - 10 Jul 2024
Event	Amitsur Centennial Symposium - Israel Institute for Advanced Studies (IIAS), Jerusalem Duration: 1 Nov 2021 → 4 Nov 2021 https://mathematics.huji.ac.il/event/amitsur-centennial-symposium

Publication series

Name	Contemporary Mathematics
Volume	800
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Conference

Conference	Amitsur Centennial Symposium
City	Jerusalem
Period	1/11/21 → 4/11/21
Internet address	https://mathematics.huji.ac.il/event/amitsur-centennial-symposium

Bibliographical note

Publisher Copyright:
© 2024 by Bar-Ilan University.

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title = "On the generation of simple groups by Sylow subgroups",

abstract = "Let G be a finite simple group of Lie type and let P be a Sylow 2-subgroup of G. In this paper, we prove that for any nontrivial element x ∈ G, there exists g ∈ G such that G = hP, xg i. By combining this result with recent work of Breuer and Guralnick, we deduce that if G is a finite nonabelian simple group and r is any prime divisor of |G|, then G is generated by a Sylow 2-subgroup and a Sylow r-subgroup",

author = "Tim Burness and Robert Guralnick",

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doi = "10.1090/conm/800/16051",

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On the generation of simple groups by Sylow subgroups. / Burness, Tim ; Guralnick, Robert.
Amitsur Centennial Symposium. ed. / Avinoam Mann; Louis H. Rowen; David J. Saltman; Aner Shalev; Lance W. Small; Uzi Vishne. American Mathematical Society, 2024. p. 81-100 (Contemporary Mathematics; Vol. 800).

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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AU - Guralnick, Robert

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N2 - Let G be a finite simple group of Lie type and let P be a Sylow 2-subgroup of G. In this paper, we prove that for any nontrivial element x ∈ G, there exists g ∈ G such that G = hP, xg i. By combining this result with recent work of Breuer and Guralnick, we deduce that if G is a finite nonabelian simple group and r is any prime divisor of |G|, then G is generated by a Sylow 2-subgroup and a Sylow r-subgroup

AB - Let G be a finite simple group of Lie type and let P be a Sylow 2-subgroup of G. In this paper, we prove that for any nontrivial element x ∈ G, there exists g ∈ G such that G = hP, xg i. By combining this result with recent work of Breuer and Guralnick, we deduce that if G is a finite nonabelian simple group and r is any prime divisor of |G|, then G is generated by a Sylow 2-subgroup and a Sylow r-subgroup

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DO - 10.1090/conm/800/16051

M3 - Conference Contribution (Conference Proceeding)

SN - 9781470475550

T3 - Contemporary Mathematics

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EP - 100

BT - Amitsur Centennial Symposium

A2 - Mann, Avinoam

A2 - Rowen, Louis H.

A2 - Saltman, David J.

A2 - Shalev, Aner

A2 - Small, Lance W.

A2 - Vishne, Uzi

PB - American Mathematical Society

T2 - Amitsur Centennial Symposium

Y2 - 1 November 2021 through 4 November 2021

ER -

On the generation of simple groups by Sylow subgroups

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