Large orbits of elements centralized by a Sylow subgroup.
type: Item
instance of: scholarly article
title: Large orbits of elements centralized by a Sylow subgroup.
zbMATH Open document ID: 1183.20020
author: Silvio Dolfi
author: Gabriel Navarro
published in: Archiv der Mathematik
publication date: 2009-11-25T00:00:00Z
review text: Let \(G\) be a finite group. In this paper, the authors prove that if \(G\) has a nilpotent normal \(p\)-complement and \(V\) is a finite, faithful and completely reducible \(G\)-module of characteristic \(p\), then there exist \(v_1,v_2 \in V\) such that \(C_G(v_1)\cap C_G(v_2)=P\), where \(P\in\text{Syl}_p(G)\). An interesting corollary is: if the normal \(p\)-complement \(K\) is non-trivial, there exists \(v\in C_V(P)\) such that \(|K:C_K(v)|^2>|K|\).
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5638426
zbMATH Keywords: large orbits
zbMATH Keywords: normal \(p\)-complements
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: completely reducible modules
reviewed by: Shi Wujie
MaRDI profile type: Publication
full work available at URL: s00013-009-0016-5
OpenAlex ID: W2021726611
cites work: Large orbits in coprime actions of solvable groups
cites work: Endliche Gruppen I
cites work: Orbit sizes of p-groups
cites work: Large orbits in actions of nilpotent groups
cites work: Q4871631
cites work: Groups with Normal, Solvable Hall p � -Subgroups
DOI: 10.1007/S00013-009-0016-5
description: scientific article; zbMATH DE number 5638426