Brauer relations in finite groups

A Bartel; Tim Dokchitser

doi:10.4171/JEMS/563

Brauer relations in finite groups

A Bartel, Tim Dokchitser

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Abstract

If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map from the Burnside ring to the representation ring of G has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tornehave-Bouc classification in the case of p-groups.

Translated title of the contribution	Brauer relations in finite groups
Original language	English
Pages (from-to)	2473-2512
Number of pages	40
Journal	Journal of the European Mathematical Society
Volume	17
Issue number	10
Early online date	28 Oct 2013
DOIs	https://doi.org/10.4171/JEMS/563
Publication status	Published - Oct 2015

Keywords

math.RT RepresentationTheory (math.GR Group Theory)

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10.4171/JEMS/563

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via EMS at http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=17&iss=10&rank=3. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 456 KBLicence: CC BY-NC

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title = "Brauer relations in finite groups",

abstract = "If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map from the Burnside ring to the representation ring of G has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tornehave-Bouc classification in the case of p-groups.",

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TY - JOUR

T1 - Brauer relations in finite groups

AU - Bartel, A

AU - Dokchitser, Tim

PY - 2015/10

Y1 - 2015/10

N2 - If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map from the Burnside ring to the representation ring of G has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tornehave-Bouc classification in the case of p-groups.

AB - If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map from the Burnside ring to the representation ring of G has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tornehave-Bouc classification in the case of p-groups.

KW - math.RT RepresentationTheory (math.GR Group Theory)

UR - http://arxiv.org/pdf/1103.2047v5

U2 - 10.4171/JEMS/563

DO - 10.4171/JEMS/563

M3 - Article (Academic Journal)

SN - 1435-9855

VL - 17

SP - 2473

EP - 2512

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 10

ER -

Brauer relations in finite groups

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