Geodesic
A class of torsion-free abelian groups characterized by the ranks of their socles
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 319-327.

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Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups, bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket $R$-module is $R$ tensor a bracket group.
Classification : 13A15, 13B22, 13C13, 13F05, 13G05, 20K15
Keywords: Dedekind domain 
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     title = {A class of torsion-free abelian groups characterized by the ranks of their socles},
     journal = {Czechoslovak Mathematical Journal},
     pages = {319--327},
     publisher = {mathdoc},
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Albrecht, Ulrich; Giovannitti, Tony; Goeters, Pat. A class of torsion-free abelian groups characterized by the ranks of their socles. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 319-327. http://geodesic.mathdoc.fr/item/CMJ_2002__52_2_a6/