The Ore conjecture.
The Ore conjecture [\textit{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.
scientific article; zbMATH DE number 5736057
scientific article