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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Martin W. Liebeck, Eamonn A. O'Brien, Aner Shalev, Pham Huu Tiep, The Ore conjecture. J. Eur. Math. Soc. 12 (2010), no. 4, pp. 939–1008DOI 10.4171/JEMS/220