Separability of the subgroups of residually nilpotent groups in the class of finite π-groups
- Authors: Sokolov E.V.1
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Affiliations:
- Ivanovo State University
- Issue: Vol 58, No 1 (2017)
- Pages: 169-175
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171021
- DOI: https://doi.org/10.1134/S0037446617010219
- ID: 171021
Cite item
Abstract
Given a nonempty set π of primes, call a nilpotent group π-bounded whenever it has a central series whose every factor F is such that: In every quotient group of F all primary components of the torsion subgroup corresponding to the numbers in π are finite. We establish that if G is a residually π-bounded torsion-free nilpotent group, while a subgroup H of G has finite Hirsh–Zaitsev rank then H is π’-isolated in G if and only if H is separable in G in the class of all finite nilpotent π-groups. By way of example, we apply the results to study the root-class residuality of the free product of two groups with amalgamation.
About the authors
E. V. Sokolov
Ivanovo State University
Author for correspondence.
Email: ev-sokolov@yandex.ru
Russian Federation, Ivanovo