THE PRO-k-SOLVABLE TOPOLOGY ON A FREE GROUP

• 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 the Australian Mathematical Society

Vol. 116

Pages: 363-383

ISSN: 1446-7887

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 0 Citations

Other information

Authenticus ID: P-00Z-QE1

DOI: 10.1017/s1446788723000162

Abstract (EN): We prove that, given a finitely generated subgroup H of a free group F, the following questions are decidable: is H closed (dense) in F for the pro-(met)abelian topology? is the closure of H in F for the pro-(met)abelian topology finitely generated? We show also that if the latter question has a positive answer, then we can effectively construct a basis for the closure, and the closure has decidable membership problem in any case. Moreover, it is decidable whether H is closed for the pro-V topology when V is an equational pseudovariety of finite groups, such as the pseudovariety S-k of all finite solvable groups with derived length <= k. We also connect the pro-abelian topology with the topologies defined by abelian groups of bounded exponent.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 21