Geodesic
Completely torsion-free, finite-rank, almost decomposable groups with torsion factor
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 61-67 
S. F. Kozhukhov; A. C. Tveretin. Completely torsion-free, finite-rank, almost decomposable groups with torsion factor. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 3, pp. 61-67. http://geodesic.mathdoc.fr/item/FPM_2007_13_3_a8/
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     title = {Completely torsion-free, finite-rank, almost decomposable groups with torsion factor},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_3_a8/}
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This paper deals with almost completely decomposable finite rank groups $G$ that have rank $1$ summands of pairwise noncomparable types. It is well known that every such group has unique complete quasi-decomposition $A$ with respect to equality. We consider the number of almost completely decomposable groups $G$ with a given quasi\df decomposition $A$ for which $G/A$ is isomorphic to $\mathbb{Z}(p^m)$.

[1] Kozhukhov S. F., “Konechnye gruppy avtomorfizmov abelevykh grupp bez krucheniya konechnogo ranga”, Izv. AN SSSR, 52:3 (1988), 501–521 | Zbl

[2] Fuks L., Beskonechnye abelevy gruppy, T. 1, Mir, M., 1974

[3] Fuks L., Beskonechnye abelevy gruppy, T. 2, Mir, M., 1977