On groups admitting a disconnected common divisor graph
type: Item
instance of: scholarly article
title: On groups admitting a disconnected common divisor graph
zbMATH Open document ID: 0891.20018
author: Gil Kaplan
published in: Journal of Algebra
publication date: 1998-07-19T00:00:00Z
review text: Let \(G\) be an arbitrary group and \(A\) be a subgroup of \(G\). Accordingly with a paper by \textit{I. M. Isaacs} and \textit{C. E. Praeger} [ibid. 159, No. 1, 158-175 (1993; Zbl 0815.20002)], the common divisor graph \(\Gamma\) associated to the pair \((G,A)\) has as vertices the subdegrees of \((G,A)\), with an edge joining two vertices if and only if they are not coprime. There it was shown that \(\Gamma\) has at most two connected components. The paper under review gives structure theorems on the behaviour of \(G\) and \(A\) in both the connected and the disconnected case. Some examples are also provided.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 1051578
zbMATH Keywords: double cosets
zbMATH Keywords: subgroups
zbMATH Keywords: common divisor graphs
zbMATH Keywords: subdegrees
zbMATH Keywords: connected components
reviewed by: Raffaele Scapellato
MaRDI profile type: Publication
full work available at URL: jabr.1996.6992
OpenAlex ID: W2045549482
cites work: On a Graph Related to Conjugacy Classes of Groups
cites work: Permutation group subdegrees and the common divisor graph
DOI: 10.1006/JABR.1996.6992
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description: scientific article; zbMATH DE number 1051578