  Let p be a prime number. This paper introduces the Roquette category R_p of
finite p-groups, which is an additive tensor category containing all finite
p-groups among its objects. In R_p, every finite p-group P admits a canonical
direct summand, called the edge of P. Moreover P splits uniquely as a direct
sum of edges of Roquette p-groups, and the tensor structure of R_p can be
described in terms of such edges. The main motivation for considering this
category is that the additive functors from R_p to abelian groups are exactly
the rational p-biset functors. This yields in particular very efficient ways of
computing such functors on arbitrary p-groups : this applies to the
representation functors R_K, where K 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.
