A characterization of 4-centralizer groups.
type: Item
instance of: scholarly article
title: A characterization of 4-centralizer groups.
zbMATH Open document ID: 1303.20038
DOI: 10.1155/2013/871072
author: Jutirekha Dutta
published in: Chinese Journal of Mathematics
publication date: 2014-10-16T00:00:00Z
review text: Summary: A finite or infinite group is called an \(n\)-centralizer group if it has \(n\) numbers of distinct centralizers. In this paper, we prove that a finite or infinite group \(G\) is a 4-centralizer group if and only if \(G/Z(G)\) is isomorphic to \(C_2 \times C_2\). This extends a result of \textit{S. M. Belcastro} and \textit{G. J. Sherman} [Math. Mag. 67, No. 5, 366-374 (1994; Zbl 0823.20023)].
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 6356631
zbMATH Keywords: 4-centralizer groups
zbMATH Keywords: numbers of centralizers
Wikidata QID: Q58920762
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/871072
OpenAlex ID: W2081406557
cites work: Q5297723
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description: scientific article; zbMATH DE number 6356631