On the closure of cyclic subgroups of a free group in some profinite topologies

• Type: Article in International Scientific Journal
• Date: 2025

Authors

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

Journal

Title: Journal of Group Theory

ISSN: 1433-5883

Publisher: Walter De Gruyter

Indexing

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Other information

Authenticus ID: P-018-FZR

DOI: 10.1515/jgth-2023-0081

Abstract (EN): We determine the closure of a cyclic subgroup H of a free group for the pro-V topology when V is an extension-closed pseudovariety of finite groups. We show that H is always closed for the pro-nilpotent topology and compute its closure for the pro-G(p) and pro- V-p topologies, where G(p) is the pseudovariety of finite p-groups and V-p superset of G(p) denote the pseudovarieties involved in the join decomposition of the pseudovariety of finite supersolvable groups. More generally, given any nonempty set P of primes, we consider the stated problem for the pseudovariety G(P) of all finite groups having order a product of primes in P.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16