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Separability of the subgroups of residually nilpotent groups in the class of finite π-groups

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 -b...

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Bibliographic Details
Published in:Siberian mathematical journal 2017, Vol.58 (1), p.169-175
Main Author: Sokolov, E. V.
Format: Article
Language:English
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Summary: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.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446617010219