Geodesic
Rank-$1$ quotient divisible groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 25-33.

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An Abelian group is called quotient divisible if it does not contain nonzero torsion divisible subgroups, but does contain a free finite rank subgroup such that the quotient group by it is divisible. In this paper, we will describe rank $1$ quotient divisible groups with the help of cocharacteristics, and we will describe the endomorphisms of these groups as well. 
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O. I. Davydova. Rank-$1$ quotient divisible groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 25-33. http://geodesic.mathdoc.fr/item/FPM_2007_13_3_a3/

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