Abstract
In the paper, representations of torsion-free Abelian groups of rank \(2\) using torsion-free groups of rank \(1\) are studied. Necessary and sufficient conditions are found under which a group given by such a representation is quotient divisible. A criterion is obtained for two \(p\)-minimal quotient divisible torsion-free groups of rank \(2\) to be isomorphic to each other. An example is constructed showing that two such groups can be embedded in each other but be nonisomorphic. A series of properties of fundamental systems of elements of quotient divisible groups of arbitrary finite rank is established.
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Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 37-51 https://doi.org/10.4213/mzm12992.
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Zonov, M.N., Timoshenko, E.A. Quotient Divisible Groups of Rank 2. Math Notes 110, 48–60 (2021). https://doi.org/10.1134/S0001434621070051
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DOI: https://doi.org/10.1134/S0001434621070051