Finite Coverings by Cosets of Normal Subgroups

Abstract

In this brief note, we characterize those groups $G$ which can be covered by finitely many cosets ${a_i}{M_i}$ of maximal normal subgroups ${M_i}$, where the covering is irredundant and not all ${M_i}$ are equal. This refines an earlier result of Brodie, Chamberlain, and Kappe, who characterized those groups which can be covered by finitely many proper normal subgroups.