Title : The Roquette category of finite p-groups

Author : Serge Bouc

Abstract : 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.