Applications of a graph related to conjugacy classes in finite groups
type: Item
instance of: scholarly article
title: Applications of a graph related to conjugacy classes in finite groups
zbMATH Open document ID: 0723.20013
DOI: 10.1007/BF01191876
author: Mariagrazia Bianchi
author: David Chillag
author: Anna Gillio Berta Mauri
author: Marcel Herzog
author: Carlo Maria Scoppola
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: A recent result of B. Huppert states that if the set of character degrees of a finite group is \(\{\) 1,2,3,...,k\(\}\) then \(k=1,2,3,4,6\). Moreover, a description of the groups for each possible k is given. Here the authors consider the analogous problem for conjugacy classes lengths and describe groups in which the lengths of the noncentral classes are consecutive integers. The proof uses the study of a graph related to conjugacy classes that was considered by Bertram, Herzog and Mann. Another application of this graph which is included here is to give a different (shorter) proof to a result of Chillag and Herzog on groups in which all noncentral classes have prime power lengths.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 4191985
zbMATH Keywords: finite group
zbMATH Keywords: conjugacy classes lengths
zbMATH Keywords: consecutive integers
zbMATH Keywords: graph
zbMATH Keywords: prime power lengths
MaRDI profile type: Publication
cites work: On a Graph Related to Conjugacy Classes of Groups
cites work: Q3659962
cites work: On the length of the conjugacy classes of finite groups
cites work: Endliche Gruppen I
cites work: A Characterization of GL(2, 3) and SL(2, 5) by the Degrees of their Representations
cites work: On Finite Groups with Given Conjugate Types I
cites work: Some p-groups of Frobenius and extra-special type
cites work: Conjugacy classes in finite groups
cites work: On the Number of Components of a Graph Related to Character Degrees
description: scientific article; zbMATH DE number 4191985