Remarks on commutators in finite groups
type: Item
instance of: scholarly article
title: Remarks on commutators in finite groups
zbMATH Open document ID: 1428.20013
author: Marian Deaconescu
author: G. L. Walls
published in: Journal für die Reine und Angewandte Mathematik
publication date: 2017-11-01T00:00:00Z
review text: Let $G$ be a finite group and let $C = \{[x, y]\mid x, y\in G\}$ be the set of all the commutators in $G$. In general, $C < G^\prime$, where $G^\prime$ is the the commutator subgroup of $G$. In this paper, the authors give a interesting formula for the number $|H \backslash C|$ whenever $H$ is a normal subgroup of $G$. The number $|G\backslash C|$ is derived as a direct consequence.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20F12
zbMATH DE Number: 6801929
reviewed by: Yangming Li
MaRDI profile type: Publication
full work available at URL: crelle-2014-0152
OpenAlex ID: W2314473638
cites work: The number of conjugacy classes in a finite group
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cites work: Q5821461
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cites work: Q3440013
DOI: 10.1515/CRELLE-2014-0152
description: scientific article; zbMATH DE number 6801929