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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Tomsk. Gos. Univ. Mat. Mekh.:
Year:
Volume:
Issue:
Page:
Find






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


Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2016, Number 3(41), Pages 42–50 (Mi vtgu526)  

This article is cited in 4 scientific papers (total in 4 papers)

MATHEMATICS

Fully inert subgroups of completely decomposable finite rank groups and their commensurability

A. R. Chekhlov

Tomsk State University, Tomsk, Russian Federation

Abstract: A subgroup $H$ of an Abelian group $G$ is said to be fully inert in $G$ if the subgroup $H\cap\varphi H$ has a finite index in $\varphi H$ for any endomorphism $\varphi$ of the group $G$. Subgroups $H$ and $K$ of the group $G$ are said to be commensurable if the subgroup $K\cap H$ has a finite index in $H$ and in $K$. Some properties of fully inert and commensurable groups in the context of direct decompositions of the group and operations on subgroups are proved. For example, if a subgroup $H$ is commensurable with a subgroup $K$, then $H$ is commensurable with $H\cap K$ and with $H + K$; if a subgroup $H$ is commensurable with a subgroup $K$, then the subgroup $fH$ is commensurable with $fK$ for any homomorphism $f$. The main result of the paper is that every fully inert subgroup of a completely decomposable finite rank torsion-free group $G$ is commensurable with a fully invariant subgroup if and only if types of rank $1$ direct summands of the group $G$ are either equal or incomparable, and all rank $1$ direct summands of the group $G$ are not divisible by any prime number $p$.

Keywords: factor group, fully invariant subgroup, commensurable subgroups, divisible hull, rank of the group.

DOI: https://doi.org/10.17223/19988621/41/4

Full text: PDF file (479 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 512.541
Received: 21.03.2016

Citation: A. R. Chekhlov, “Fully inert subgroups of completely decomposable finite rank groups and their commensurability”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2016, no. 3(41), 42–50

Citation in format AMSBIB
\Bibitem{Che16}
\by A.~R.~Chekhlov
\paper Fully inert subgroups of completely decomposable finite rank groups and their commensurability
\jour Vestn. Tomsk. Gos. Univ. Mat. Mekh.
\yr 2016
\issue 3(41)
\pages 42--50
\mathnet{http://mi.mathnet.ru/vtgu526}
\crossref{https://doi.org/10.17223/19988621/41/4}
\elib{http://elibrary.ru/item.asp?id=26224725}


Linking options:
  • http://mi.mathnet.ru/eng/vtgu526
  • http://mi.mathnet.ru/eng/vtgu/y2016/i3/p42

    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. R. Chekhlov, “On Fully Inert Subgroups of Completely Decomposable Groups”, Math. Notes, 101:2 (2017), 365–373  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. R. Chekhlov, “On Strongly Invariant Subgroups of Abelian Groups”, Math. Notes, 102:1 (2017), 106–110  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. R. Chekhlov, “Intermediately fully invariant subgroups of abelian groups”, Siberian Math. J., 58:5 (2017), 907–914  mathnet  crossref  crossref  isi  elib  elib
    4. U. Dardano, D. Dikranjan, S. Rinauro, “Inertial properties in groups”, Int. J. Group Theory, 7:3, 3 (2018), 17–62  crossref  mathscinet  isi
  • Вестник Томского государственного университета. Математика и механика
    Number of views:
    This page:195
    Full text:29
    References:27

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