Geodesic
On the Question of the Definability of Certain Classes of Completely Decomposable Abelian Torsion-Free Groups by Their Homomorphism Groups
Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 738-741

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

Let $C$ be an Abelian group. A class $X$ is said to be a $_{C}H$-class if, for any groups $A,B\in X$, a group isomorphism of $\operatorname{Hom}(C,A)$ and $\operatorname{Hom}(C,B)$ implies an isomorphism of the groups $A$ and $B$. In the paper, conditions on a completely decomposable Abelian group $C$ are investigated under which a class of certain completely decomposable torsion-free Abelian groups is a $_{C}H$-class.
Keywords: completely decomposable Abelian group, definability of Abelian groups.
Mots-clés : homomorphism group 
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     author = {T. A. Pushkova and A. M. Sebel'din},
     title = {On the {Question} of the {Definability} of {Certain} {Classes} of {Completely} {Decomposable} {Abelian} {Torsion-Free} {Groups} by {Their} {Homomorphism} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {738--741},
     publisher = {mathdoc},
     volume = {113},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a8/}
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T. A. Pushkova; A. M. Sebel'din. On the Question of the Definability of Certain Classes of Completely Decomposable Abelian Torsion-Free Groups by Their Homomorphism Groups. Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 738-741. http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a8/