The Ore conjecture
Martin W. Liebeck
Imperial College, London, UKEamonn A. O'Brien
The University of Auckland, New ZealandAner Shalev
The Hebrew University of Jerusalem, IsraelPham Huu Tiep
University of Arizona, Tucson, USA
Abstract
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.
Cite this article
Martin W. Liebeck, Eamonn A. O'Brien, Aner Shalev, Pham Huu Tiep, The Ore conjecture. J. Eur. Math. Soc. 12 (2010), no. 4, pp. 939–1008
DOI 10.4171/JEMS/220