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Commutators in finite quasisimple groups
Author(s) -
Liebeck Martin W.,
O'Brien E. A.,
Shalev Aner,
Tiep Pham Huu
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdr043
Subject(s) - mathematics , commutator , conjecture , abelian group , simple (philosophy) , pure mathematics , classification of finite simple groups , simple group , group (periodic table) , finite group , algebra over a field , group of lie type , group theory , physics , philosophy , lie conformal algebra , epistemology , quantum mechanics
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 A 6 , A 7 , L 3 (4) and U 4 (3).