JournalsjemsVol. 17, No. 10pp. 2473–2512

Brauer relations in finite groups

  • Alex Bartel

    University of Warwick, Coventry, UK
  • Tim Dokchitser

    University of Bristol, UK
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Abstract

If GG is a non-cyclic finite group, non-isomorphic GG-sets X,YX, Y may give rise to isomorphic permutation representations C[X]C[Y]\mathbb C[X ]\cong \mathbb C[Y]. Equivalently, the map from the Burnside ring to the rational representation ring of GG 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 pp-groups.

Cite this article

Alex Bartel, Tim Dokchitser, Brauer relations in finite groups. J. Eur. Math. Soc. 17 (2015), no. 10, pp. 2473–2512

DOI 10.4171/JEMS/563