Brauer relations in finite groups II - quasi-elementary groups of order p^aq

TL;DR

This paper advances the understanding of Brauer relations in finite groups by classifying primitive relations specifically for quasi-elementary groups of order p^a q, building on prior work that identified primitive relations generally.

Contribution

It provides a detailed classification of primitive Brauer relations for quasi-elementary groups of order p^a q, which was previously not explicitly described in terms of generators and relations.

Findings

Classified primitive Brauer relations for quasi-elementary groups of order p^a q

Extended the previous classification to include explicit group descriptions

Enhanced understanding of the structure of Brauer relations in specific finite groups

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 do this for quasi-elementary groups of order p^aq.