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

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

2011-12-26

arxiv.org/abs/1112.5892v1

Mathematics

Group Theory

Scientific paper

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 $\sigma(\Aut(PSL(2,8)))=29$.

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