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The Ore conjecture. (English) Zbl 1205.20011
The Ore conjecture [Ø. Ore, Proc. Am. Math. Soc. 2, 307-314 (1951; Zbl 0043.02402)] 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 long paper the authors develop new strategies, combining character theoretic methods with other ingredients, and use them to complete the proof of this conjecture.
Reviewer: Shi Wujie (Suzhou)

MSC:
20D06 Simple groups: alternating groups and groups of Lie type
20F12 Commutator calculus
20C33 Representations of finite groups of Lie type
20F05 Generators, relations, and presentations of groups
Software:
Magma; GAP
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