Commutators in finite quasisimple groups

Martin W. Liebeck; E. A. O'Brien; Aner Shalev; Pham Huu Tiep

doi:10.1112/blms/bdr043

Commutators in finite quasisimple groups

Martin W. Liebeck
, E. A. O'Brien
, Aner Shalev
, Pham Huu Tiep

Mathematics

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

23 Scopus citations

Abstract

The Ore Conjecture, now established, states that every element of every finite non-abelian simple group is a commutator. We prove that the same result holds for all the finite quasisimple groups, with a short explicit list of exceptions. In particular, the only quasisimple groups with non-central elements which are not commutators are covers of A6, A7, L3(4) and U4(3).

Original language	English (US)
Pages (from-to)	1079-1092
Number of pages	14
Journal	Bulletin of the London Mathematical Society
Volume	43
Issue number	6
DOIs	https://doi.org/10.1112/blms/bdr043
State	Published - Dec 2011

ASJC Scopus subject areas

General Mathematics

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title = "Commutators in finite quasisimple groups",

abstract = "The Ore Conjecture, now established, states that every element of every finite non-abelian simple group is a commutator. We prove that the same result holds for all the finite quasisimple groups, with a short explicit list of exceptions. In particular, the only quasisimple groups with non-central elements which are not commutators are covers of A6, A7, L3(4) and U4(3).",

author = "Liebeck, \{Martin W.\} and O'Brien, \{E. A.\} and Aner Shalev and Tiep, \{Pham Huu\}",

note = "Funding Information: Liebeck acknowledges the support of a Maclaurin Fellowship from the New Zealand Institute of Mathematics and its Applications. O{\textquoteright}Brien acknowledges the support of the Marsden Fund of New Zealand (grant UOA 0721). Shalev acknowledges the support of an ERC Advanced Grant 247034, an EPSRC Visiting Fellowship, an Israel Science Foundation Grant, and a Bi-National Science Foundation grant United States-Israel. Tiep acknowledges the support of the NSF (grant DMS-0901241).",

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AU - Liebeck, Martin W.

AU - O'Brien, E. A.

AU - Shalev, Aner

AU - Tiep, Pham Huu

N1 - Funding Information: Liebeck acknowledges the support of a Maclaurin Fellowship from the New Zealand Institute of Mathematics and its Applications. O’Brien acknowledges the support of the Marsden Fund of New Zealand (grant UOA 0721). Shalev acknowledges the support of an ERC Advanced Grant 247034, an EPSRC Visiting Fellowship, an Israel Science Foundation Grant, and a Bi-National Science Foundation grant United States-Israel. Tiep acknowledges the support of the NSF (grant DMS-0901241).

PY - 2011/12

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N2 - The Ore Conjecture, now established, states that every element of every finite non-abelian simple group is a commutator. We prove that the same result holds for all the finite quasisimple groups, with a short explicit list of exceptions. In particular, the only quasisimple groups with non-central elements which are not commutators are covers of A6, A7, L3(4) and U4(3).

AB - The Ore Conjecture, now established, states that every element of every finite non-abelian simple group is a commutator. We prove that the same result holds for all the finite quasisimple groups, with a short explicit list of exceptions. In particular, the only quasisimple groups with non-central elements which are not commutators are covers of A6, A7, L3(4) and U4(3).

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JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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Commutators in finite quasisimple groups

Abstract

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