The functor of units of Burnside rings for p-groups

Details The functor of units of Burnside rings for p-groups The functor of units of Burnside rings for p-groups

2006-07-27

arxiv.org/abs/math/0607703v1

Mathematics

Group Theory

Scientific paper

In this note I describe the structure of the biset functor $B^\times$ sending a $p$-group $P$ to the group of units of its Burnside ring $B(P)$. In particular, I show that $B^\times$ is a rational biset functor. It follows that if $P$ is a $p$-group, the structure of $B^\times(P)$ can be read from a genetic basis of $P$: the group $B^\times(P)$ 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.

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