Finite groups in which no two distinct conjugacy classes have the same order
type: Item
instance of: scholarly article
title: Finite groups in which no two distinct conjugacy classes have the same order
zbMATH Open document ID: 0663.20021
DOI: 10.1007/BF01198104
author: Michael B. Ward
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: How many nontrivial groups are described by the title of the paper? Probably only one: \(S_ 3\). - In this note, the author proves \(S_ 3\) is the only finite \(\{\) 2,3\(\}\)-group in which no two distinct conjugacy classes have the same order. The strategy is simple. Show that the existence of certain ``large'' conjugacy classes implies the group is isomorphic to \(S_ 3\) and then show that the class equation insures the presence of these ``large'' classes. This result generalizes two other published papers on the same topic.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 4083902
zbMATH Keywords: finite \(\{\) 2,3\(\}\) -group
zbMATH Keywords: conjugacy classes
zbMATH Keywords: order
zbMATH Keywords: class equation
MaRDI profile type: Publication
cites work: Groups whose characters are rational-valued
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cites work: On Centralizers of Involutions
cites work: Structure and representations of Q-groups
cites work: Groups with many conjugate elements
cites work: On finite groups containing an element of order four which commutes only with its powers
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description: scientific article; zbMATH DE number 4083902