On groups that are dominated by countably many proper subgroups
type: Item
instance of: scholarly article
title: On groups that are dominated by countably many proper subgroups
zbMATH Open document ID: 1437.20021
author: Giovanni Cutolo
author: Derek J. S. Robinson
author: Ahmet Arıkan
published in: Journal of Algebra
publication date: 2018-06-18T00:00:00Z
review text: In the article under review, the authors study the structure of a group having a countably set of proper subgroups with the property that every proper subgroup is contained in some member of the set (such a group is called \(\mathbf{CD}\)-\textit{group}). In the article, the authors first give various examples of \(\mathbf{CD}\)-groups. Further, some classes of groups with \(\mathbf{CD}\) property are described. Among them, all virtually nilpotent \(\mathbf{CD}\)-groups are characterized. Some aspects of soluble \(\mathbf{CD}\)-groups is also studied. If every subgroup of a \(\mathbf{CD}\)-group \(G\) is a \(\mathbf{CD}\)-group, then \(G\) is called \(\mathbf{SCD}\)-\textit{group}. In the article, examples of \(\mathbf{CD}\)-groups are given that are not \(\mathbf{SCD}\). A theorem describing all soluble \(\mathbf{SCD}\)-groups is also given.
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 6890671
zbMATH Keywords: proper subgroup
zbMATH Keywords: countably dominated set
reviewed by: Bùi Xuân Hải
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2018.05.018
OpenAlex ID: W2803143168
cites work: On locally graded non-periodic barely transitive groups.
cites work: On groups with countably many maximal subgroups
cites work: Groups with descending chain condition for normal subgroups
cites work: Irreducible groups of automorphisms of abelian groups
cites work: Q5789191
cites work: Groups with countably many subgroups.
cites work: Q4856782
cites work: A dual approach to Černikov modules
cites work: Uncountable Artinian Modules and Uncountable Soluble Groups Satisfying Min-n
cites work: Injective modules and soluble groups satisfying the minimal condition for normal subgroups
cites work: Q4820338
cites work: Soluble groups with the minimum condition for normal subgroups
cites work: Q5654235
Wikidata QID: Q129807108
DOI: 10.1016/J.JALGEBRA.2018.05.018
description: scientific article; zbMATH DE number 6890671