The Ore conjecture

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

Research output: Contribution to journalArticle

91 Citations (Scopus)

Abstract

The Ore conjecture, posed in 1951, 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 paper we develop new strategies, combining character-theoretic methods with other ingredients, and use them to establish the conjecture.

Original languageEnglish (US)
Pages (from-to)939-1008
Number of pages70
JournalJournal of the European Mathematical Society
Volume12
Issue number4
DOIs
StatePublished - 2010

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Electric commutators
Simple group
Ores
Commutator
Strategy
Character
Family

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

The Ore conjecture. / Liebeck, Martin W.; O'Brien, E. A.; Shalev, Aner; Tiep, Pham Huu.

In: Journal of the European Mathematical Society, Vol. 12, No. 4, 2010, p. 939-1008.

Research output: Contribution to journalArticle

Liebeck, MW, O'Brien, EA, Shalev, A & Tiep, PH 2010, 'The Ore conjecture', Journal of the European Mathematical Society, vol. 12, no. 4, pp. 939-1008. https://doi.org/10.4171/JEMS/22G
Liebeck, Martin W. ; O'Brien, E. A. ; Shalev, Aner ; Tiep, Pham Huu. / The Ore conjecture. In: Journal of the European Mathematical Society. 2010 ; Vol. 12, No. 4. pp. 939-1008.
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