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The Ore conjecture

2010; European Mathematical Society; Volume: 12; Issue: 4 Linguagem: Inglês

10.4171/jems/22g

1435-9863

Martin W. Liebeck, E. A. O’Brien, Aner Shalev, Pham Huu Tiep,

Geometric and Algebraic Topology

The Ore conjecture, posed in 1951, states that every element of every finite non-abelian simple group is a commutator. Despite considerable effort, it remains 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. Liebeck acknowledges the support of a Maclaurin Fellowship from the New Zealand Institute of Mathematics and its Applications. O’Brien acknowledges the support of an LMS Visitor Grant, the Marsden Fund of New Zealand (grant UOA 0721), and the Mathematical Sciences Research Institute (Berkeley). Shalev acknowledges the support of an EPSRC Visiting Fellowship, an Israel Science Foundation Grant, and a Bi-National Science Foundation grant United States-Israel 2004-052. Tiep acknowledges the support of the NSF (grant DMS-0600967), and the Mathematical Sciences Research Institute (Berkeley).