Products of squares in finite simple groups

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

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

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
Volume140
Issue number1
DOIs
StatePublished - 2012

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Electric commutators
Finite Simple Group
Ores
Simple group
Commutator
Lagrange
High Power
Analogue
Theorem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Products of squares in finite simple groups. / Liebeck, Martin W.; O'brien, E. A.; Shalev, Aner; Tiep, Pham Huu.

In: Proceedings of the American Mathematical Society, Vol. 140, No. 1, 2012, p. 21-33.

Research output: Contribution to journalArticle

Liebeck, Martin W. ; O'brien, E. A. ; Shalev, Aner ; Tiep, Pham Huu. / Products of squares in finite simple groups. In: Proceedings of the American Mathematical Society. 2012 ; Vol. 140, No. 1. pp. 21-33.
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