The Roquette category of finite pp-groups

  • Serge Bouc

    Université de Picardie - Jules Verne, Amiens, France


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

The main motivation for considering this category is that the additive functors from Rp\mathcal{R}_p to abelian groups are exactly the rational pp-biset functors. This yields in particular very efficient ways of computing such functors on arbitrary pp-groups: this applies to the representation functors RKR_K, where KK 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 pp-groups. J. Eur. Math. Soc. 17 (2015), no. 11, pp. 2843–2886

DOI 10.4171/JEMS/573