A useful category for mixed Abelian groups.
Abelian Factorizations of Infinite Groups.
Abelian group extensions and the axiom of constructibility.
Abelian group pairs having a trivial coGalois group
Torsion-free covers are considered for objects in the category Objects in the category are just maps in -Mod. For we find necessary and sufficient conditions for the coGalois group associated to a torsion-free cover, to be trivial for an object in Our results generalize those of E. Enochs and J. Rado for abelian groups.
Abelian groups have/are near Frattini subgroups
The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups.
Abelian groups in a topos of sheaves: Torsion and essential extensions.
Abelian groups in which every pure subgroup is an isotype subgroup
Abelian groups in which every -isotype subgroup is a pure subgroup, resp. an isotype subgroup
Abelian groups of zero adjoint entropy
The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of zero adjoint...
Abelian groups that cannot be factored without periodic factor
Abelian groups which have trivial absolute coGalois group
In this article we characterize those abelian groups for which the coGalois group (associated to a torsion free cover) is equal to the identity.
Abelian groups whose endomorphism ring is linearly compact
Abelian Groups with an Endomorphism with Irreducible minimum Polynomial
Abelian groups with anti-isomorphic endomorphism rings
Abelian groups with many automorphisms
Abelian pro-countable groups and orbit equivalence relations
We study a class of abelian groups that can be defined as Polish pro-countable groups, as non-archimedean groups with a compatible two-sided invariant metric or as quasi-countable groups, i.e., closed subdirect products of countable discrete groups, endowed with the product topology. We show that for every non-locally compact, abelian quasi-countable group G there exists a closed L ≤ G and a closed, non-locally compact K ≤ G/L which is a direct product of discrete countable groups....
Abelian torsion groups with a pseudocompact group topology.
Abelian torsion groups with artinian primary components and their automorphisms
AE-rings
Algebraic Classes of Abelian Torsion-Free and Lattice-Ordered Groups