Journal of the European Mathematical Society

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Volume 12, Issue 4, 2010, pp. 939–1008
DOI: 10.4171/JEMS/220

The Ore conjecture

Martin W. Liebeck[1], Eamonn A. O'Brien[2], Aner Shalev[3] and Pham Huu Tiep[4]

(1) Department of Mathematics, Imperial College, South Kensington Campus, SW7 2BZ, LONDON, UNITED KINGDOM
(2) Department of Mathematics, The University of Auckland, Private Bag 92019, 1142, AUCKLAND, NEW ZEALAND
(3) Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904, JERUSALEM, ISRAEL
(4) Department of Mathematics, University of Arizona, 617 N Santa Rita, AZ 85721, TUCSON, UNITED STATES

The Ore conjecture, posed in 1951, states that every element of every finite non-abelian simple group is a commutator. Despite considerable effort, it remained open for various infinite families of simple groups. In this paper we develop new strategies, combining character-theoretic methods with other ingredients, and use them to establish the conjecture.

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Liebeck Martin, O'Brien Eamonn, Shalev Aner, Tiep Pham: The Ore conjecture. J. Eur. Math. Soc. 12 (2010), 939-1008. doi: 10.4171/JEMS/220