## Ladislav Bican

*Butler groups and Shelah's Singular Compactness *

Comment.Math.Univ.Carolinae 37,1 (1996) 169-176. **Abstract:**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.

**Keywords:** $B_1$-group, $B_2$-group, prebalanced subgroup, torsion extension property, decent subgroup, axiom-3 family

**AMS Subject Classification:** 20K20

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