Indices of centralizers for Hall-subgroups of linear groups
type: Item
instance of: scholarly article
title: Indices of centralizers for Hall-subgroups of linear groups
zbMATH Open document ID: 0930.20010
author: Thomas Wolf
published in: Illinois Journal of Mathematics
publication date: 2000-02-10T00:00:00Z
review text: For a nontrivial Sylow-\(p\)-subgroup of a solvable transitive permutation group \(G\) of degree \(n\), we show that the number of \(P\)-orbits is at most \(2n/(p+1)\). This in turn is used to prove that whenever \(G\) is a solvable irreducible linear group of degree \(n\) with Sylow-\(p\)-subgroup \(P>1\), then the dimension of the centralizer of \(P\) is at most \(2n/(p+1)\). This generalizes (and provides alternate proofs of) results of Isaacs and Navarro. It is also used to affirmatively answer a question of Pérez Monasor and Iranzo Aznar regarding indices of centralizers in coprime operator groups.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20B20
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 1333067
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: solvable transitive permutation groups
zbMATH Keywords: numbers of orbits
zbMATH Keywords: solvable irreducible linear groups
zbMATH Keywords: indices of centralizers
zbMATH Keywords: coprime operator groups
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1333067