The functor of units of Burnside rings for -groups

  • Serge Bouc

    Université de Picardie - Jules Verne, Amiens, France

Abstract

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

Cite this article

Serge Bouc, The functor of units of Burnside rings for -groups. Comment. Math. Helv. 82 (2007), no. 3, pp. 583–615

DOI 10.4171/CMH/103