Minimal coverings of completely reducible groups

Abstract

Let G be a group that is a set-theortic union of finitely many proper subgroups. Cohn defined σ(G) to be the least integer m such that G is the union of m proper subgroups. Determining σ is an open problem for most non-solvable groups. In this paper we give a formula for σ(G), where G is a completely reducible group.