Tensor products and units of partial Burnside rings

Abstract

In this paper, we study tensor products of partial Burnside rings relative to collections of subgroups of finite groups. We give a necessary and sufficient condition for the canonical homomorphism from the directproduct of the unit groups to the unit group of the tensor product to be surjective. We also describe the decomposition of the sign unit of a reducible finite Coxeter group.

arXiv comment14 pages