RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirsk. Mat. Zh., 2017, Volume 58, Number 1, Pages 219–229 (Mi smj2854)  

This article is cited in 2 scientific papers (total in 2 papers)

Separability of the subgroups of residually nilpotent groups in the class of finite $\pi$-groups

E. V. Sokolov

Ivanovo State University, Ivanovo, Russia

Abstract: Given a nonempty set $\pi$ of primes, call a nilpotent group $\pi$-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 $\pi$ are finite. We establish that if $G$ is a residually $\pi$-bounded torsion-free nilpotent group, while a subgroup $H$ of $G$ has finite Hirsh–Zaitsev rank then $H$ is $\pi'$-isolated in $G$ if and only if $H$ is separable in $G$ in the class of all finite nilpotent $\pi$-groups. By way of example, we apply the results to study the root-class residuality of the free product of two groups with amalgamation.

Keywords: separable subgroups, residual nilpotency, residual $\pi$-finiteness, free product with amalgamation, root classes of groups.

DOI: https://doi.org/10.17377/smzh.2017.58.121

Full text: PDF file (318 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2017, 58:1, 169–175

Bibliographic databases:

UDC: 512.543
MSC: 20E26, 20E06, 20F22
Received: 13.03.2016

Citation: E. V. Sokolov, “Separability of the subgroups of residually nilpotent groups in the class of finite $\pi$-groups”, Sibirsk. Mat. Zh., 58:1 (2017), 219–229; Siberian Math. J., 58:1 (2017), 169–175

Citation in format AMSBIB
\Bibitem{Sok17}
\by E.~V.~Sokolov
\paper Separability of the subgroups of residually nilpotent groups in the class of finite $\pi$-groups
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 1
\pages 219--229
\mathnet{http://mi.mathnet.ru/smj2854}
\crossref{https://doi.org/10.17377/smzh.2017.58.121}
\elib{http://elibrary.ru/item.asp?id=29159917}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 1
\pages 169--175
\crossref{https://doi.org/10.1134/S0037446617010219}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000396065100021}
\elib{http://elibrary.ru/item.asp?id=29488862}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014721408}


Linking options:
  • http://mi.mathnet.ru/eng/smj2854
  • http://mi.mathnet.ru/eng/smj/v58/i1/p219

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. E. Kuvaev, “Neobkhodimye usloviya nilpotentnoi approksimiruemosti nekotorykh teoretiko-gruppovykh konstruktsii”, Sib. matem. zhurn., 60:6 (2019), 1335–1349  mathnet  crossref
    2. E. V. Sokolov, E. A. Tumanova, “Ob approksimiruemosti kornevymi klassami nekotorykh svobodnykh proizvedenii grupp s normalnymi ob'edinennymi podgruppami”, Izv. vuzov. Matem., 2020, no. 3, 48–63  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
    Number of views:
    This page:65
    Full text:14
    References:16
    First page:5

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020