The Ore conjecture

  • Martin W. Liebeck

    Imperial College, London, UK
  • Eamonn A. O'Brien

    The University of Auckland, New Zealand
  • Aner Shalev

    The Hebrew University of Jerusalem, Israel
  • Pham Huu Tiep

    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.

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