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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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Published in: | Siberian mathematical journal 2017, Vol.58 (1), p.169-175 |
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Main Author: | |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0037-4466 1573-9260 |
DOI: | 10.1134/S0037446617010219 |