Prime factors of conjugacy-class lengths and irreducible character-degrees in finite soluble groups.
type: Item
instance of: scholarly article
title: Prime factors of conjugacy-class lengths and irreducible character-degrees in finite soluble groups.
zbMATH Open document ID: 0833.20010
author: Silvio Dolfi
published in: Journal of Algebra
publication date: 1995-08-29T00:00:00Z
review text: There are intimate connections between the sets \(cd(G)\) of the irreducible character-degrees and \(cl(G)\) of the conjugacy class-lengths of \(G\). The main result in that direction proved here, is: Theorem. Let \(G\) be a solvable group and \(p\), \(q\) two distinct primes. If the product \(pq\) divides the degree of some irreducible character of \(G\), then \(pq\) divides also the length of some conjugacy class of \(G\).
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 783887
zbMATH Keywords: finite soluble groups
zbMATH Keywords: irreducible character-degrees
zbMATH Keywords: conjugacy class-lengths
zbMATH Keywords: solvable groups
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
full work available at URL: jabr.1995.1150
OpenAlex ID: W2070947217
DOI: 10.1006/JABR.1995.1150
description: scientific article; zbMATH DE number 783887