Relative -Groups

  • Serge Bouc

    LAMFA-CNRS, Université de Picardie Jules Verne, 33 rue St Leu, F-80039 Amiens, France
Relative $B$-Groups cover
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This paper extends the notion of -group to a relative context. For a finite group and a field of characteristic 0, the lattice of ideals of the Green biset functor obtained by shifting the Burnside functor by is described in terms of -groups. It is shown that any finite group over admits a largest quotient -group . The simple subquotients of are parametrized by -groups, and their evaluations can be precisely determined. Finally, when is a prime, the restriction of to finite -groups is considered, and the structure of the lattice of ideals of the Green functor is described in full detail. In particular, it is shown that this lattice is always finite.

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Serge Bouc, Relative -Groups. Doc. Math. 24 (2019), pp. 2431–2462

DOI 10.4171/DM/730