The Roquette category of finite -groups

  • Serge Bouc

    Université de Picardie - Jules Verne, Amiens, France


Let be a prime number. This paper introduces the Roquette category of finite -groups, which is an additive tensor category containing all finite -groups among its objects. In , every finite -group admits a canonical direct summand , called the edge of . Moreover splits uniquely as a direct sum of edges of Roquette -groups, and the tensor structure of can be described in terms of such edges.

The main motivation for considering this category is that the additive functors from to abelian groups are exactly the rational -biset functors. This yields in particular very efficient ways of computing such functors on arbitrary -groups: this applies to the representation functors , where is any field of characteristic 0, but also to the functor of units of Burnside rings, or to the torsion part of the Dade group.

Cite this article

Serge Bouc, The Roquette category of finite -groups. J. Eur. Math. Soc. 17 (2015), no. 11, pp. 2843–2886

DOI 10.4171/JEMS/573