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Brauer relations in finite groups

Alex Bartel, Tim Dokchitser (2015)

Journal of the European Mathematical Society

If G is a non-cyclic finite group, non-isomorphic G -sets X , Y may give rise to isomorphic permutation representations [ X ] [ 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.

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