Geodesic
Butler groups and Shelah's Singular Compactness
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 1, pp. 171-178.

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A torsion-free group is a $B_2$-group if and only if it has an axiom-3 family $\frak C$ of decent subgroups such that each member of $\frak C$ has such a family, too. Such a family is called $SL_{\aleph_0}$-family. Further, a version of Shelah's Singular Compactness having a rather simple proof is presented. As a consequence, a short proof of a result [R1] stating that a torsion-free group $B$ in a prebalanced and TEP exact sequence $0 \to K \to C \to B \to 0$ is a $B_2$-group provided $K$ and $C$ are so.
Classification : 20K20, 20K27
Keywords: $B_1$-group; $B_2$-group; prebalanced subgroup; torsion extension property; decent subgroup; axiom-3 family 
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Bican, Ladislav. Butler groups and Shelah's Singular Compactness. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 1, pp. 171-178. http://geodesic.mathdoc.fr/item/CMUC_1996__37_1_a11/