Products of squares in finite simple groups

Martin W. Liebeck, E. A. O'brien, Aner Shalev, Pham Huu Tiep

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


The Ore conjecture, proved by the authors, states that every element of every finite non-abelian simple group is a commutator. In this paper we use similar methods to prove that every element of every finite simple group is a product of two squares. This can be viewed as a non-commutative analogue of Lagrange's four squares theorem. Results for higher powers are also obtained.

Original languageEnglish (US)
Pages (from-to)21-33
Number of pages13
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - 2012

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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