Some simple biset functors.

Let 푝 be a prime number, let 퐻 be a finite 푝-group, and let 픽 be a field of characteristic 0, considered as a trivial F ⁢ Out ⁢ (H) -module. The main result of this paper gives the dimension of the evaluation S H , F ⁢ (G) of the simple biset functor S H , F at an arbitrary finite group 퐺. A closely related result is proved in the last section: for each prime number 푝, 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 푝-elementary subgroups of 퐺. [ABSTRACT FROM AUTHOR]