Rational p-biset functors

In this paper, I give several characterizations of rational biset functors over p-groups, which are independent of the knowledge of genetic bases for p-groups. I also introduce a construction of new biset functors from known ones, which is similar to the Yoneda construction for representable functors, and to the Dress construction for Mackey functors, and I show that this construction preserves the class of rational p-biset functors. This leads to a characterization of rational p-biset functors as additive functors from a specific quotient category of the biset category to abelian groups. Finally, I give a description of the largest rational quotient of the Burnside p-biset functor: when p is odd, this is simply the functor R-Q of rational representations, but when p = 2, it is a non-split extension of R-Q by a specific uniserial functor, which happens to be closely related to the functor of units of the Burnside ring. (C) 2007 Elsevier Inc. All rights reserved.