# Brauer relations in finite groups

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 10, page 2473-2512
- ISSN: 1435-9855

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topBartel, Alex, and Dokchitser, Tim. "Brauer relations in finite groups." Journal of the European Mathematical Society 017.10 (2015): 2473-2512. <http://eudml.org/doc/277675>.

@article{Bartel2015,

abstract = {If $G$ is a non-cyclic finite group, non-isomorphic $G$-sets $X, Y$ may give rise to isomorphic permutation representations $\mathbb \{C\}[X ]\cong \mathbb \{C\}[Y]$. Equivalently, the map from the Burnside ring to the rational 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.},

author = {Bartel, Alex, Dokchitser, Tim},

journal = {Journal of the European Mathematical Society},

keywords = {Brauer relations; finite groups; permutation groups; Burnside ring; rational representations; finite groups; permutation permutation representations; Burnside ring; Brauer relations},

language = {eng},

number = {10},

pages = {2473-2512},

publisher = {European Mathematical Society Publishing House},

title = {Brauer relations in finite groups},

url = {http://eudml.org/doc/277675},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Bartel, Alex

AU - Dokchitser, Tim

TI - Brauer relations in finite groups

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 10

SP - 2473

EP - 2512

AB - If $G$ is a non-cyclic finite group, non-isomorphic $G$-sets $X, Y$ may give rise to isomorphic permutation representations $\mathbb {C}[X ]\cong \mathbb {C}[Y]$. Equivalently, the map from the Burnside ring to the rational 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.

LA - eng

KW - Brauer relations; finite groups; permutation groups; Burnside ring; rational representations; finite groups; permutation permutation representations; Burnside ring; Brauer relations

UR - http://eudml.org/doc/277675

ER -

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