The Ore conjecture.
type: Item
instance of: scholarly article
title: The Ore conjecture.
zbMATH Open document ID: 1205.20011
DOI: 10.4171/JEMS/220
author: Martin W. Liebeck
author: E. A. O'Brien
author: Aner Shalev
author: Pham Huu Tiep
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2010-07-13T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: The Ore conjecture [\textit{Ø. Ore}, Proc. Am. Math. Soc. 2, 307-314 (1951; Zbl 0043.02402)] 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 long paper the authors develop new strategies, combining character theoretic methods with other ingredients, and use them to complete the proof of this conjecture.
reviewed by: Shi Wujie
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20F12
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 5736057
zbMATH Keywords: finite nonabelian simple groups
zbMATH Keywords: commutators
zbMATH Keywords: characters
Wikidata QID: Q105335539
describes a project that uses: Magma
describes a project that uses: GAP
MaRDI profile type: Publication
cites work: Involutions in Chevalley groups over fields of even order
cites work: A Fixed-Point Theorem for Central Elements in Quasisimple Groups
cites work: Q4851596
cites work: The Magma algebra system. I: The user language
cites work: Computing conjugacy class representatives in permutation groups.
cites work: Q3682663
cites work: Generating random elements of a finite group
cites work: Q3684278
cites work: The centralizers of semisimple elements of the Chevalley groups \(E_ 7\) and \(E_ 8\)
cites work: Q3997911
cites work: Q5645586
cites work: On the conjectures of J. Thompson and O. Ore
cites work: Q3846428
cites work: The semisimple conjugacy classes and the generic class number of the finite simple groups of lie type E8
cites work: The semisimple conjugacy classes of finite groups of lie type E6and E7
cites work: Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements.
cites work: Commutator maps, measure preservation, and 𝑇-systems
cites work: Weil representations associated to finite fields
cites work: Sharper character value estimates for groups of Lie type
cites work: Commutators in the symplectic group
cites work: Commutators in Finite Simple Groups of Lie Type
cites work: Cross characteristic representations of even characteristic symplectic groups
cites work: Nilpotency in classical groups over a field of characteristic 2
cites work: Q3996618
cites work: Subgroups of Maximal Rank in Finite Exceptional Groups of Lie Type
cites work: Subgroups generated by root elements in groups of Lie type
cites work: Reductive subgroups of exceptional algebraic groups
cites work: Q3117579
cites work: Character degrees and random walks in finite groups of Lie type
cites work: SMALLEST DEGREES OF REPRESENTATIONS OF EXCEPTIONAL GROUPS OF LIE TYPE
cites work: Q4183492
cites work: The conjugate classes of unipotent elements of the Chevalley groups \(E_ 7\) and \(E_ 8\).
cites work: Degrees of rational characters of finite groups.
cites work: Low-Dimensional Complex Characters of the Symplectic and Orthogonal Groups
cites work: Q5679022
cites work: Some Remarks on Commutators
cites work: Word maps, conjugacy classes, and a noncommutative Waring-type theorem.
cites work: Rank 3 permutation modules of the finite classical groups.
cites work: Q5662587
cites work: Commutators in the Special and General Linear Groups
cites work: Q3293441
description: scientific article; zbMATH DE number 5736057