On boundedly generated subgroups of profinite groups

Covato, Elisa

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