Maximal subgroups of direct products

Jacques Thévenaz

Maximal subgroups of direct products

群论 2008-02-03 v1

作者: Jacques Thévenaz

摘要

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~ $\sc G^n$ .

引用

@article{arxiv.math/9703201,
  title  = {Maximal subgroups of direct products},
  author = {Jacques Thévenaz},
  journal= {arXiv preprint arXiv:math/9703201},
  year   = {2008}
}

备注

Plain TeX file, 8 pages

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