Brauer relations in finite groups II: Quasi-elementary groups of order paq

Abstract

Abstract. This is the second in a series of papers investigating the space of Brauer relations of a finite group, the kernel of the natural map from its Burnside ring to the rational representation ring. The first paper classified all primitive Brauer relations, that is those that do not come from proper subquotients. In the case of quasi-elementary groups the description is intricate, and it does not specify groups that have primitive relations in terms of generators and relations. In this paper we provide such a classification in terms of generators and relations for quasi-elementary groups of order paq.