Some simple biset functors

Let p be a prime number, let H be a finite p-group, and let F be a field of characteristic 0, considered as a trivial FOut(H)-module. The main result of this paper gives the dimension of the evaluation S-H,S-F(G) of the simple biset functor S-H,S-F at an arbitrary finite group G. A closely related result is proved in the last section: for each prime number p, a Green biset functor E-p is introduced, as a specific quotient of the Burnside functor, and it is shown that the evaluation E-p(G) is a free abelian group of rank equal to the number of conjugacy classes of p-elementary subgroups of G.