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On a class of locally Butler groups

Ladislav Bican (1991)

Commentationes Mathematicae Universitatis Carolinae

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.

On countable extensions of primary abelian groups

Peter Vassilev Danchev (2007)

Archivum Mathematicum

It is proved that if A is an abelian p -group with a pure subgroup G so that A / G is at most countable and G is either p ω + n -totally projective or p ω + n -summable, then A is either p ω + n -totally projective or p ω + n -summable as well. Moreover, if in addition G is nice in A , then G being either strongly p ω + n -totally projective or strongly p ω + n -summable implies that so is A . This generalizes a classical result of Wallace (J. Algebra, 1971) for totally projective p -groups as well as continues our recent investigations in (Arch....

On extensions of bounded subgroups in Abelian groups

S. S. Gabriyelyan (2014)

Commentationes Mathematicae Universitatis Carolinae

It is well-known that every bounded Abelian group is a direct sum of finite cyclic subgroups. We characterize those non-trivial bounded subgroups H of an infinite Abelian group G , for which there is an infinite subgroup G 0 of G containing H such that G 0 has a special decomposition into a direct sum which takes into account the properties of G , and which induces a natural decomposition of H into a direct sum of finite subgroups.

On extensions of primary almost totally projective abelian groups

Peter Vassilev Danchev (2008)

Mathematica Bohemica

Suppose G is a subgroup of the reduced abelian p -group A . The following two dual results are proved: ( * ) If A / G is countable and G is an almost totally projective group, then A is an almost totally projective group. ( * * ) If G is countable and nice in A such that A / G is an almost totally projective group, then A is an almost totally projective group. These results somewhat strengthen theorems due to Wallace (J. Algebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively.

On localizations of torsion abelian groups

José L. Rodríguez, Jérôme Scherer, Lutz Strüngmann (2004)

Fundamenta Mathematicae

As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of LT is bounded by | T | ℵ ₀ whenever T is torsion abelian and L is a localization functor. In this paper we study localizations of torsion abelian groups and investigate new examples. In particular we prove that the structure of LT is determined by the structure of the localization of the primary components of T in many cases. Furthermore, we completely characterize the relationship...

On Some Fully Invariant Subgroups of Summable Groups

Peter Danchev (2008)

Annales mathématiques Blaise Pascal

We show the inheritance of summable property for certain fully invariant subgroups by the whole group and vice versa. The results are somewhat parallel to these due to Linton (Mich. Math. J., 1975) and Linton-Megibben (Proc. Amer. Math. Soc., 1977). They also generalize recent assertions of ours in (Alg. Colloq., 2009) and (Bull. Allah. Math. Soc., 2008)

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