Almost completely decomposable groups with primary cyclic regulating quotient
Almost totally projective groups
An alternative proof of Hill's criterion of freeness for Abelian groups.
An axiomatic approach for the Hajós theorem.
Basic subgroups in modular abelian group algebras
Suppose is a perfect field of and is an arbitrary abelian multiplicative group with a -basic subgroup and -component . Let be the group algebra with normed group of all units and its Sylow -subgroup , and let be the nilradical of the relative augmentation ideal of with respect to . The main results that motivate this article are that is basic in , and is -basic in provided is -mixed. These achievements extend in some way a result of N. Nachev (1996) in Houston...
Butler groups and Shelah's Singular Compactness
A torsion-free group is a -group if and only if it has an axiom-3 family of decent subgroups such that each member of has such a family, too. Such a family is called -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 in a prebalanced and TEP exact sequence is a -group provided and are so.
Butler groups cannot be classified by certain invariants
Butler groups of infinite rank
Butler groups of infinite rank and axiom 3
Butler groups, valuated vector spaces, and duality
Centers of -isotypity in abelian groups
Characterization of the inessential endomorphisms in the category of Abelian group.
An endomorphism f of an Abelian group A is said to be inessentia! (in the category of Abelian groups) if it can be extended to an endomorphism of any Abelian group which contains A as a subgroup. In this paper we show that f is as above if and only if (f - v idA)(A) is contained in the rnaximal divisible subgroup of A for some v belonging to Z.
Classification of torsion free abelian minimax groups
Cobalanced exact sequences
Commutative group algebras of highly torsion-complete abelian -groups
A new class of abelian -groups with all high subgroups isomorphic is defined. Commutative modular and semisimple group algebras over such groups are examined. The results obtained continue our recent statements published in Comment. Math. Univ. Carolinae (2002).
Commutativity Criterions using Normal Subgroup Lattices
Completely decomposable pure subgroups of completely decomposable abelian groups
Das Gewicht einer Butlergruppe.
Direct decompositions and basic subgroups in commutative group rings
An attractive interplay between the direct decompositions and the explicit form of basic subgroups in group rings of abelian groups over a commutative unitary ring are established. In particular, as a consequence, we give a simpler confirmation of a more general version of our recent result in this aspect published in Czechoslovak Math. J. (2006).
Einige Ergebnisse aus der Theorie der zyklisch erzeugten modularen Verbände