Year: 1997
Type: preprint
Abstract: 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~$\sc G^n$.
Source: arXiv (Cornell University)
Author: Thévenaz, Jacques
Institution: University of Lausanne
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952209884