The pro-supersolvable topology on a free group: Deciding denseness

• Type: Article in International Scientific Journal
• Date: 2024

Authors

Marion, C (Author) Other; Pedro V. Silva (Author) FCUP; Tracey, G (Author) Other

Journal

Title: Journal of Algebra

Vol. 646

Pages: 183-204

ISSN: 0021-8693

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-010-0N1

DOI: 10.1016/j.jalgebra.2024.02.002

Abstract (EN): Let F be a free group of arbitrary rank and let H be a finitely generated subgroup of F. Given a pseudovariety V of finite groups, i.e. a class of finite groups closed under taking subgroups, quotients and finitary direct products, we endow F with its pro -V topology. Our main result states that it is decidable whether H is pro -Su dense, where Su subset of S denote respectively the pseudovarieties of all finite supersolvable groups and all finite solvable groups. Our motivation stems from the following open problem: is it decidable whether H is pro -S dense? (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 22