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

• Tipo: Artigo em Revista Científica Internacional
• Data: 2025

Autores

Marion, C (Autor) Outra; Pedro V. Silva (Autor) FCUP; Tracey, G (Autor) Outra

Revista

Título: Journal of Group Theory

ISSN: 1433-5883

Editora: Walter De Gruyter

Indexação

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Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 16