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

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

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

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} 

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

 SHARE:

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
2. A. R. Chekhlov, “On Strongly Invariant Subgroups of Abelian Groups”, Math. Notes, 102:1 (2017), 106–110
3. A. R. Chekhlov, “Intermediately fully invariant subgroups of abelian groups”, Siberian Math. J., 58:5 (2017), 907–914
4. U. Dardano, D. Dikranjan, S. Rinauro, “Inertial properties in groups”, Int. J. Group Theory, 7:3, 3 (2018), 17–62
•  Number of views: This page: 195 Full text: 29 References: 27