Journal of the European Mathematical Society

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

Published online: 2010-06-02

The Ore conjecture

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

(1) Imperial College, London, UK
(2) The University of Auckland, New Zealand
(3) The Hebrew University of Jerusalem, Israel
(4) University of Arizona, Tucson, USA

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