Commutators, words, conjugacy classes and character methods

Aner Shalev*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

23 Scopus citations


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.

Original languageAmerican English
Pages (from-to)131-148
Number of pages18
JournalTurkish Journal of Mathematics
Issue numberSUPPL.
StatePublished - Dec 2007


  • Characters
  • Commutators
  • Conjagacy classes
  • Finite simple groups
  • Random walks
  • Word maps


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