The Ore conjecture

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

doi:10.4171/jems/220

The Ore conjecture

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

Mathematics

Research output: Contribution to journal › Article › peer-review

158 Scopus citations

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 language	English (US)
Pages (from-to)	939-1008
Number of pages	70
Journal	Journal of the European Mathematical Society
Volume	12
Issue number	4
DOIs	https://doi.org/10.4171/jems/220
State	Published - 2010

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4171/jems/220

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title = "The Ore conjecture",

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.",

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AU - Liebeck, Martin W.

AU - O'Brien, E. A.

AU - Shalev, Aner

AU - Tiep, Pham Huu

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

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UR - https://www.scopus.com/pages/publications/77954912738#tab=citedBy

U2 - 10.4171/jems/220

DO - 10.4171/jems/220

M3 - Article

AN - SCOPUS:77954912738

SN - 1435-9855

VL - 12

SP - 939

EP - 1008

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 4

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The Ore conjecture

Abstract

ASJC Scopus subject areas

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