Finite Groups that are the union of at most 25 proper subgroups

Martino Garonzi

Finite Groups that are the union of at most 25 proper subgroups

Group Theory 2011-12-30 v1

Authors: Martino Garonzi

Abstract

For a finite group $G$ let $\sigma(G)$ (the "sum" of $G$ ) be the least number of proper subgroups of $G$ whose set-theoretical union is equal to $G$ , and $\sigma(G)=\infty$ if $G$ is cyclic. We say that a group $G$ is $\sigma$ -elementary if for every non-trivial normal subgroup $N$ of $G$ we have $\sigma(G)<\sigma(G/N)$ . In this paper we produce the list of all the $\sigma$ -elementary groups of sum up to 25. We also show that $\sigma(\Aut(PSL(2,8)))=29$ .

Keywords

finite group proper subgroup cyclic group normal subgroup sigma-elementary

Cite

@article{arxiv.1112.5892,
  title  = {Finite Groups that are the union of at most 25 proper subgroups},
  author = {Martino Garonzi},
  journal= {arXiv preprint arXiv:1112.5892},
  year   = {2011}
}

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