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¡M¡ of maximal normal subgroups Mi, where the covering is irredundant and not all M¡ 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.[8]).In this paper, we seek to extend Theorem 1, as stated above, to coverings by cosets of normal subgroups.As a by-product of this investigation, we obtain a different (perhaps simpler) proof of Theorem 1 than that given in [3].

Locations

• Proceedings of the American Mathematical Society - View - PDF