Brauer relations in finite groups

Bartel, 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 -