Almost Butler groups

Abstract

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 [BR] stating that a group G of weakly compact cardinality λ having a λ-filtration consisting of pure B 2-subgroup is a B 2-group appears as a corollary.