The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Almost Butler groups”

Butler groups and Shelah's Singular Compactness

Ladislav Bican (1996)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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 → K → C → B → 0 is a B 2 -group provided K and C are so.

A property of B 2 -groups

Kulumani M. Rangaswamy (1994)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

It is shown, under ZFC, that a B 2 -group has the interesting property of being ℵ 0 -prebalanced in every torsion-free abelian group in which it is a pure subgroup. As a consequence, we obtain alternate proofs of some well-known theorems on B 2 -groups.

Some generalizations of torsion-free Crawley groups

Brendan Goldsmith, Fatemeh Karimi, Ahad Mehdizadeh Aghdam (2013)

Czechoslovak Mathematical Journal

Similarity:

In this paper we investigate two new classes of torsion-free Abelian groups which arise in a natural way from the notion of a torsion-free Crawley group. A group G is said to be an Erdős group if for any pair of isomorphic pure subgroups H , K with G / H ≅ G / K , there is an automorphism of G mapping H onto K ; it is said to be a weak Crawley group if for any pair H , K of isomorphic dense maximal pure subgroups, there is an automorphism mapping H onto K . We show that these classes are extensive and pay...

On a class of locally Butler groups

Ladislav Bican (1991)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A torsionfree abelian group B is called a Butler group if B e x t ( B , T ) = 0 for any torsion group T . It has been shown in [DHR] that under C H any countable pure subgroup of a Butler group of cardinality not exceeding ℵ ω is again Butler. The purpose of this note is to show that this property has any Butler group which can be expressed as a smooth union ∪ α < μ B α of pure subgroups B α having countable typesets.