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Title: Butler groups and Shelah's Singular Compactness (English)
Author: Bican, Ladislav
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 37
Issue: 1
Year: 1996
Pages: 171-178
Category: math
Summary: 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. (English)
Keyword: $B_1$-group
Keyword: $B_2$-group
Keyword: prebalanced subgroup
Keyword: torsion extension property
Keyword: decent subgroup
Keyword: axiom-3 family
MSC: 20K20
MSC: 20K27
idZBL: Zbl 0857.20037
idMR: MR1396169
Date available: 2009-01-08T18:22:49Z
Last updated: 2012-04-30
Stable URL:
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