A graph related to conjugacy classes of solvable groups
type: Item
instance of: scholarly article
title: A graph related to conjugacy classes of solvable groups
zbMATH Open document ID: 0840.20012
author: Guy Alfandary
published in: Journal of Algebra
publication date: 1996-06-30T00:00:00Z
review text: Consider the graph \(\Gamma^* (G)\) related to the finite group \(G\) defined so that its vertices are the prime divisors of the sizes of conjugacy classes and two vertices are connected if they both divide the size of some conjugacy class. The author then considers two subgroups, induced respectively on the set of primes \(p\) for which the normalizer Sylow \(p\)-group is the centralizer and those primes for which it is not. He proves that these two graphs are complete for soluble groups unless they contain a section with a very specific structure.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 815923
zbMATH Keywords: graphs
zbMATH Keywords: finite groups
zbMATH Keywords: conjugacy classes
zbMATH Keywords: Sylow \(p\)-groups
zbMATH Keywords: soluble groups
reviewed by: A. R. Camina
MaRDI profile type: Publication
full work available at URL: jabr.1995.1257
OpenAlex ID: W2000918953
DOI: 10.1006/JABR.1995.1257
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description: scientific article; zbMATH DE number 815923