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Butler groups and Shelah's Singular Compactness

Ladislav Bican (1996)

Commentationes Mathematicae Universitatis Carolinae

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.

We characterize a particular kind of decomposition of a Butler group that is the general case for Butler B(1)-groups; and exhibit a decomposition of a B(2)-group which is not of that kind.

Butler groups, valuated vector spaces, and duality

Fred Richman (1984)

Rendiconti del Seminario Matematico della Università di Padova

Displaying 141 – 146 of 146

Butler groups and Shelah's Singular Compactness

Butler groups cannot be classified by certain invariants

Butler groups of infinite rank

Butler groups of infinite rank and axiom 3

Butler groups splitting over a base element

Butler groups, valuated vector spaces, and duality

Currently displaying 141 – 146 of 146