Relative Brauer relations of abelian p-groups

Marian F. Anton

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arXiv · 2112.10331

Relative Brauer relations of abelian p-groups

Marian F. Anton

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Abstract

The Brauer relations of a finite group $G$ are virtual differences of non-isomorphic $G$-sets $X-Y$ which induce isomorphic permutation $G$-representations $\mathbb Q[X]\simeq\mathbb Q[Y]$ over the rationals. These relations have been classified by Tornehave-Bouc and Bartel-Dokchitser. Motivated by stable homotopy theory, a relative version of Brauer relations for $(G,C_p)$-bisets which are $C_p$-free have been classified by Kahn in case $G$ is an elementary Abelian $p$-group. In this paper we extend Kahn's classification to the case when $G$ is a finite Abelian $p$-group.

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BibTeX RIS

Marian F. Anton. 2021-12-20. Relative Brauer relations of abelian p-groups. https://arxiv.org/abs/2112.10331

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