Rings of functions on non-abelian groups

Abstract

For several classes of finite nonabelian groups we investigate the structure of the ring of functions, \({\mathcal{R}(C)}\), determined by the cover \(C\) of maximal abelian subgroups. We determine the Jacobson radical \(J({\mathcal{R}(C))}\) and the semisimple quotient ring \({\mathcal{R}(C)}/J({\mathcal{R}(C))}\).