Commutators in finite quasisimple groups

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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 languageAmerican English
Pages (from-to)1079-1092
Number of pages14
JournalBulletin of the London Mathematical Society
Issue number6
StatePublished - Dec 2011

Bibliographical note

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).


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