The functor of units of Burnside rings for p-groups

By Serge Bouc. 2006

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/10cd9360168d4caea5fd315ce76e346f11d27ca0