Geodesic
On determinability of a completely decomposable rank $2$ group by its automorphism group
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 68 (2020), pp. 23-32

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Necessary and sufficient conditions are found under which two completely decomposable torsion-free Abelian groups of rank $2$ have isomorphic automorphism groups. An answer is obtained to the question of under what conditions a completely decomposable Abelian group of rank $2$ is uniquely determined by its group of automorphisms.
Mots-clés : matrix, automorphism group.
Keywords: involution, completely decomposable group 
V. K. Vildanov; V. A. Gaidak; E. A. Timoshenko. On determinability of a completely decomposable rank $2$ group by its automorphism group. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 68 (2020), pp. 23-32. http://geodesic.mathdoc.fr/item/VTGU_2020_68_a1/
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     title = {On determinability of a completely decomposable rank $2$ group by its automorphism group},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
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     year = {2020},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2020_68_a1/}
}
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[1] Gaidak V.A., Timoshenko E.A., “Involutions of the general linear group $GL_2$ over a subring of the field $\mathbf{Q}$”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics, 2019, no. 62, 19–26 | DOI | MR

[2] Vildanov V.K., “Determinability of completely decomposable torsionfree Abelian group of rank 2 by its automorphism group”, Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo – Vestnik of Lobachevsky State University of Nizhny Novgorod, 2011, no. 3(1), 174–177

[3] Fuchs L., Infinite Abelian groups, v. 2, Academic Press, New York–London, 1973 | MR | Zbl