On the Theory and Classification of Abelian p-Groups.
Properties of subgroups not containing their centralizers
In this paper, we give a generalization of Baer Theorem on the injective property of divisible abelian groups. As consequences of the obtained result we find a sufficient condition for a group to express as semi-direct product of a divisible subgroup and some subgroup . We also apply the main Theorem to the -groups with center of index , for some prime . For these groups we compute the number of conjugacy classes and the number of abelian maximal subgroups and the number of nonabelian...
Pure subgroups
Let be an infinite cardinal. Set , define for every , take as the first cardinal with , and put . If is a torsion-free group of cardinality at least and is its subgroup such that is torsion and , then contains a non-zero subgroup pure in . This generalizes the result from a previous paper dealing with -primary.
Pure subgroups split
Purely finitely generated Abelian groups
Quasi-balanced torsion-free groups
An exact sequence of torsion-free abelian groups is quasi-balanced if the induced sequence is exact for all rank-1 torsion-free abelian groups . This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which is a Butler group. The special case where is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced...
Quasibases of -groups
Quasi-essential subsocles of Abelian p-groups
Regularität in torsionsfreien abelschen Gruppen
Regulierende Untergruppen und der Regulator fast vollständig zerlegbarer Gruppen
Schichtengleiche Gewichte und Butlergruppen
Self-pseudoprojective completely decomposable Abelian groups.
Separable and vector groups whose projectively invariant subgroups are fully invariant.
Separable mixed groups
Some generalizations of torsion-free Crawley groups
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 is said to be an Erdős group if for any pair of isomorphic pure subgroups with , there is an automorphism of mapping onto ; it is said to be a weak Crawley group if for any pair of isomorphic dense maximal pure subgroups, there is an automorphism mapping onto . We show that these classes are extensive and pay attention to...
Splitting in abelian groups
Splittings of infinite abelian group.
Splittings of infinite abelian group. (Short Communication).
Square subgroups of rank two abelian groups
Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.
Strong -groups