Maximal subgroups of direct products

Details Maximal subgroups of direct products Maximal subgroups of direct products

1997-03-10

arxiv.org/abs/math/9703201v1

Mathematics

Group Theory

Plain TeX file, 8 pages

Scientific paper

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

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