Residual Separability of Subgroups in Free Products with Amalgamated Subgroup of Finite Index
- Authors: Kryazheva A.A.1
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Affiliations:
- Ivanovo State University
- Issue: Vol 60, No 2 (2019)
- Pages: 319-324
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172343
- DOI: https://doi.org/10.1134/S0037446619020125
- ID: 172343
Cite item
Abstract
Let P be the free product of groups A and B with amalgamated subgroup H, where H is a proper subgroup of finite index in A and B. We assume that the groups A and B satisfy a nontrivial identity and for each natural n the number of all subgroups of index n in A and B is finite. We prove that all cyclic subgroups in P are residually separable if and only if P is residually finite and all cyclic subgroups in H are residually separable; and all finitely generated subgroups in P are residually separable if and only if P is residually finite and all subgroups that are the intersections of H with finitely generated subgroups of P are finitely separable in H.
About the authors
A. A. Kryazheva
Ivanovo State University
Author for correspondence.
Email: Stasia.07.10@mail.ru
Russian Federation, Ivanovo