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On boundedly generated subgroups of profinite groups

Covato, Elisa

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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. © 2014 Elsevier Inc.

Journal Article Type Article
Online Publication Date Mar 17, 2014
Publication Date May 15, 2014
Deposit Date Apr 25, 2024
Journal Journal of Algebra
Print ISSN 0021-8693
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 406
Pages 20-45
DOI https://doi.org/10.1016/j.jalgebra.2014.02.019
Public URL https://uwe-repository.worktribe.com/output/11915350


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