## Maximal subgroups of direct products

We determine all maximal subgroups of the direct product G^n of n copies of a group G. If G is finite, we show that the number of maximal subgroups of G^n is a quadratic function of n if G is perfect, but grows exponentially otherwise. We deduce a theorem of Wiegold about the growth behaviour of the number of generators of G^n.

Published in:
Journal of Algebra, 198, 2, 352-361
Year:
1997
Keywords:
Laboratories: