Geodesic
Correctness of Abelian torsion-free groups and determinability of Abelian groups by their subgroups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2014), pp. 16-29

Voir la notice de l'article provenant de la source Math-Net.Ru

An Abelian group $A$ is called correct if for any Abelian group $B$ isomorphisms $A\cong B'$ and $B\cong A'$, where $A'$ and $B'$ are subgroups of the groups $A$ and $B$, respectively, imply the isomorphism $A\cong B$. We say that a group $A$ is determined by its subgroups (its proper subgroups) if for any group $B$ the existence of a bijection between the sets of all subgroups (all proper subgroups) of groups $A$ and $B$ such that corresponding subgroups are isomorphic implies $A\cong B$. In this paper, connections between the correctness of Abelian groups and their determinability by their subgroups (their proper subgroups) are established. Certain criteria of determinability of divisible torsion-free groups and completely decomposable groups by their subgroups and their proper subgroups, as well as a criterion of correctness of such groups, are obtained.
Keywords: almost isomorphism, correctness of Abelian groups, determinability of Abelian groups by their subgroups (their proper subgroups).
Mots-clés : $s$-isomorphism, $t$-isomorphism 
@article{VTGU_2014_5_a1,
     author = {S. Ya. Grinshpon and A. K. Mordovskoi},
     title = {Correctness of {Abelian} torsion-free groups and determinability of {Abelian} groups by their subgroups},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {16--29},
     publisher = {mathdoc},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2014_5_a1/}
}
TY  - JOUR
AU  - S. Ya. Grinshpon
AU  - A. K. Mordovskoi
TI  - Correctness of Abelian torsion-free groups and determinability of Abelian groups by their subgroups
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2014
SP  - 16
EP  - 29
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTGU_2014_5_a1/
LA  - ru
ID  - VTGU_2014_5_a1
ER  - 
%0 Journal Article
%A S. Ya. Grinshpon
%A A. K. Mordovskoi
%T Correctness of Abelian torsion-free groups and determinability of Abelian groups by their subgroups
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2014
%P 16-29
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTGU_2014_5_a1/
%G ru
%F VTGU_2014_5_a1
S. Ya. Grinshpon; A. K. Mordovskoi. Correctness of Abelian torsion-free groups and determinability of Abelian groups by their subgroups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2014), pp. 16-29. http://geodesic.mathdoc.fr/item/VTGU_2014_5_a1/