On socle-regularity and some notions of transitivity for Abelian \(p\)-groups.

DOI10.1216/JCA-2011-3-3-301zbMath1247.20062OpenAlexW2004872351MaRDI QIDQ412548

Peter V. Danchev, Brendan Goldsmith

Publication date: 4 May 2012

Published in: Journal of Commutative Algebra (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jca/1313973573

zbMATH Keywords

Abelian \(p\)-groupscharacteristic subgroupsfully invariant subgroupsfully transitive groupsKrylov transitive groupsstrongly socle-regular groupsweakly transitive groups

Mathematics Subject Classification ID

Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Torsion groups, primary groups and generalized primary groups (20K10) Subgroups of abelian groups (20K27)

Related Items (12)

FULLY TRANSITIVE, TRANSITIVE ABELIAN GROUPS AND SOME THEIR GENERALIZATIONS ⋮ On transitivity-like properties for torsion-free abelian groups ⋮ On projectively fully transitive Abelian \(p\)-groups. ⋮ On Abelian groups with commuting monomorphisms. ⋮ Some transitivity-like concepts in abelian groups ⋮ Fully inert subgroups of Abelian \(p\)-groups. ⋮ Generalizations of fully transitive and valuated abelian \(p\)-groups ⋮ On some properties of endomorphism rings of abelian groups ⋮ On abelian groups with commutative commutators of endomorphisms ⋮ On projectively fully transitive abelian groups ⋮ On projectively Krylov transitive and projectively weakly transitive abelian \(p\)-groups ⋮ On commutator Krylov transitive and commutator weakly transitive abelian \(p\)-groups

Cites Work

• On the socles of characteristic subgroups of Abelian \(p\)-groups.
• On the socles of fully invariant subgroups of Abelian \(p\)-groups.
• Centers of purity in Abelian groups
• THE INDEPENDENCE OF KAPLANSKY'S NOTIONS OF TRANSITIVITY AND FULL TRANSITIVITY
• Transitive and fully transitive groups
• On Transitive and Fully Transitive Primary Groups
• Some Results on Abelian Groups
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