Geodesic
Quotient Divisible Groups of Rank~2
Matematičeskie zametki, Tome 110 (2021) no. 1, pp. 37-51

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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 not isomorphic. A series of properties of fundamental systems of elements of quotient divisible groups of arbitrary finite rank is established.
Keywords: Abelian group, group of rank $2$.
Mots-clés : quotient divisible group, quotient divisible envelope 
@article{MZM_2021_110_1_a3,
     author = {M. N. Zonov and E. A. Timoshenko},
     title = {Quotient {Divisible} {Groups} of {Rank~2}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {37--51},
     publisher = {mathdoc},
     volume = {110},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a3/}
}
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M. N. Zonov; E. A. Timoshenko. Quotient Divisible Groups of Rank~2. Matematičeskie zametki, Tome 110 (2021) no. 1, pp. 37-51. http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a3/