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- W4300792311 abstract "In this paper we investigate the following general problem. Let $G$ be a group and let $i(G)$ be a property of $G$. Is there an integer $d$ such that $G$ contains a $d$-generated subgroup $H$ with $i(H)=i(G)$? Here we consider the case where $G$ is a profinite group and $H$ is a closed subgroup, extending earlier work of Lucchini and others on finite groups. For example, we prove that $d=3$ if $i(G)$ is the prime graph of $G$, which is best possible, and we show that $d=2$ if $i(G)$ is the exponent of a finitely generated prosupersolvable group $G$." @default.
- W4300792311 created "2022-10-04" @default.
- W4300792311 creator A5000419841 @default.
- W4300792311 date "2013-12-30" @default.
- W4300792311 modified "2023-10-16" @default.
- W4300792311 title "On boundedly generated subgroups of profinite groups" @default.
- W4300792311 doi "https://doi.org/10.48550/arxiv.1312.7689" @default.
- W4300792311 hasPublicationYear "2013" @default.
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