Maximal Subgroups of Direct Products

Abstract

We determine all maximal subgroups of the direct productGnofncopies of a groupG. IfGis finite, we show that the number of maximal subgroups ofGnis a quadratic function ofnifGis perfect, but grows exponentially otherwise. We deduce a theorem of Wiegold about the growth behaviour of the number of generators ofGn. © 1997 Academic Press.