2006/07/27 by Bouc, Serge · 1 citation
#16U60 #19A22 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.math/0607703
In this note 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.