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 ${\mathcal{R}(C)}/J({\mathcal{R}(C))}$.