The functor of units of Burnside rings for <var>p</var>-groups

Abstract

In this paper, I describe the structure of the biset functor B× sending a p-group P to the group of units of its Burnside ring B(P). In particular, I show that B× is a rational biset functor. It follows that if P is a p-group, the structure of B×(P) can be read from a genetic basis of P: the group B×(P) is an elementary abelian 2-group of rank equal to the number isomorphism classes of rational irreducible representations of P whose type is trivial, cyclic of order 2, or dihedral.