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Article

Bican, Ladislav
Almost Butler groups. (English). Czechoslovak Mathematical Journal, vol. 50 (2000), issue 2, pp. 367-378
MSC: 20K20, 20K27 | MR 1761394 | Zbl 1051.20023
Summary:
Generalizing the notion of the almost free group we introduce almost Butler groups. An almost $B_2$-group $G$ of singular cardinality is a $B_2$-group. Since almost $B_2$-groups have preseparative chains, the same result in regular cardinality holds under the additional hypothesis that $G$ is a $B_1$-group. Some other results characterizing $B_2$-groups within the classes of almost $B_1$-groups and almost $B_2$-groups are obtained. A theorem of stating that a group $G$ of weakly compact cardinality $\lambda $ having a $\lambda $-filtration consisting of pure $B_2$-subgroup is a $B_2$-group appears as a corollary.
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