Fully invariant subgroups, full transitivity, and homomorphism groups of Abelian groups.

DOI10.1007/s10958-005-0245-5zbMath1131.20041OpenAlexW2089876411MaRDI QIDQ997785

S. Ya. Grinshpon, Piotr A. Krylov

Publication date: 7 August 2007

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-005-0245-5

zbMATH Keywords

endomorphismsdirect sumsautomorphismsdirect productsfully invariant subgroupslattices of fully invariant subgroups\(H\)-groupsfully transitive Abelian groupsheight matrices

Mathematics Subject Classification ID

Chains and lattices of subgroups, subnormal subgroups (20E15) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Direct sums, direct products, etc. for abelian groups (20K25) Subgroups of abelian groups (20K27) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

Related Items (20)

Counting compact group topologies ⋮ Injective modules over formal matrix rings. ⋮ On the full transitivity of a cotorsion hull ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The lattice of fully invariant subgroups of a cotorsion hull ⋮ Full transitivity condition for the cotorsion hull. ⋮ The lattice of fully invariant subgroups of the cotorsion hull. ⋮ The Lattice of U-Sequences of an Abelian p-Group ⋮ Modules over discrete valuation domains. III ⋮ Modules over discrete valuation domains. I ⋮ Abelian groups isomorphic to a proper fully invariant subgroup ⋮ The lattice of fully invariant subgroups of a cotorsion group ⋮ On projectively fully transitive abelian groups ⋮ On a property of Abelian groups related to direct sums and products. ⋮ Colocalizations and dualities for modules and Abelian groups. ⋮ The lattice of fully invariant subgroups of a cotorsion group. ⋮ Modules over discrete valuation domains. II ⋮ On \(K\)-large and generalized \(K\)-large Abelian groups.

Cites Work

• Strongly homogeneous torsion-free Abelian groups
• A generalization of separable torsion-free Abelian groups
• Distributive rings and endodistributive modules
• A sufficient condition for separability
• Finite rank torsion free Abelian groups and rings
• Distributive modules
• Quasi-pure projective and injective torsion free Abelian groups of rank 2
• E-transitive torsion-free Abelian groups
• The flat dimension of mixed abelian groups as \(E\)-modules
• Rings of endomorphisms and distributivity
• Primary abelian groups as modules over their endomorphism rings
• C\(_{\gamma}\)-groups and \(\gamma\)-basic subgroups
• The homological dimension of an Abelian group as a module over its ring of endomorphisms. II
• On -separable abelian groups
• Modules Whose Lattice of Submodules is Distributive
• THE INDEPENDENCE OF KAPLANSKY'S NOTIONS OF TRANSITIVITY AND FULL TRANSITIVITY
• ON ENDOMORPHISM RINGS OF PRIMARY ABELIAN GROUPS, II
• Strongly Homogeneous Torsion Free Abelian Groups of Finite Rank
• Transitive and fully transitive groups
• Modules whose lattice of submodules is distributive
• FLATNESS AND THE RING OF QUASI-ENDOMORPHISMS
• On Transitive and Fully Transitive Primary Groups
• The structure of large subgroups of primary abelian groups
• Types of Elements and Characteristic Subgroups of Abelian Groups
• Endomorphism rings of Abelian groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Fully invariant subgroups, full transitivity, and homomorphism groups of Abelian groups.