On socle-regularity and some notions of transitivity for Abelian \(p\)-groups.
type: Item
instance of: scholarly article
title: On socle-regularity and some notions of transitivity for Abelian \(p\)-groups.
zbMATH Open document ID: 1247.20062
DOI: 10.1216/JCA-2011-3-3-301
published in: Journal of Commutative Algebra
publication date: 2012-05-04T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jca/1313973573
review text: In this clearly written paper, the authors describe four notions of transitivity for reduced Abelian \(p\)-groups and derive the connections among them. They relate these properties to the concepts of (strongly) socle-regular groups.
reviewed by: Phillip Schultz
Mathematics Subject Classification ID: 20K10
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 20K27
zbMATH DE Number: 6030523
zbMATH Keywords: Abelian \(p\)-groups
zbMATH Keywords: fully invariant subgroups
zbMATH Keywords: characteristic subgroups
zbMATH Keywords: fully transitive groups
zbMATH Keywords: Krylov transitive groups
zbMATH Keywords: weakly transitive groups
zbMATH Keywords: strongly socle-regular groups
author: Peter Danchev
author: B. Goldsmith
MaRDI profile type: Publication
cites work: Q4342195
cites work: THE INDEPENDENCE OF KAPLANSKY'S NOTIONS OF TRANSITIVITY AND FULL TRANSITIVITY
cites work: On the socles of fully invariant subgroups of Abelian \(p\)-groups.
cites work: On the socles of characteristic subgroups of Abelian \(p\)-groups.
cites work: Transitive and fully transitive groups
cites work: Q5609457
cites work: Q5438371
cites work: On Transitive and Fully Transitive Primary Groups
cites work: Some Results on Abelian Groups
cites work: Q5829819
cites work: Centers of purity in Abelian groups
cites work: Q3734710
OpenAlex ID: W2004872351
description: scientific article; zbMATH DE number 6030523