In this survey paper we show how character methods can be used to solve a wide range of seemingly unrelated problems. These include commutators, powers of conjugacy classes and related random walks, as well as word maps and Waring type problems. In particular we describe recent progress made on conjectures of Ore, of Thompson, and of Lulov and Pak. New open problems and conjectures are also stated.
Finite simple groups, commutators, conjagacy classes, characters, word maps, random walks
SHALEV, ANER (2007) "Commutators, Words, Conjugacy Classes and Character Methods," Turkish Journal of Mathematics: Vol. 31: No. 5, Article 10. Available at: https://journals.tubitak.gov.tr/math/vol31/iss5/10