Geodesic
Torsion-free Abelian groups with cyclic $p$-basic subgroups
Matematičeskie zametki, Tome 20 (1976) no. 6, pp. 805-813.

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We investigate the structure of indecomposable torsion-free Abelian groups all of whose $p$-basic subgroups are cyclic, and also the structure of the groups and rings of endomorphisms of such groups. We prove the existence of a torsion-free Abelian group of countable rank with cyclic $p$-basic subgroups which has no indecomposable nonzero direct summands. 
@article{MZM_1976_20_6_a1,
     author = {P. A. Krylov},
     title = {Torsion-free {Abelian} groups with cyclic $p$-basic subgroups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {805--813},
     publisher = {mathdoc},
     volume = {20},
     number = {6},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_6_a1/}
}
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P. A. Krylov. Torsion-free Abelian groups with cyclic $p$-basic subgroups. Matematičeskie zametki, Tome 20 (1976) no. 6, pp. 805-813. http://geodesic.mathdoc.fr/item/MZM_1976_20_6_a1/