A property of $B_2$-groups

Kulumani M. Rangaswamy

Displaying similar documents to “A property of $B_{2}$ -groups”

Butler groups and Shelah's Singular Compactness

Ladislav Bican (1996)

Commentationes Mathematicae Universitatis Carolinae

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A torsion-free group is a $B_{2}$ -group if and only if it has an axiom-3 family $ℭ$ of decent subgroups such that each member of $ℭ$ has such a family, too. Such a family is called $S L_{ℵ_{0}}$ -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.