Über eine Bemerkung von Glauberman. (On a remark of Glauberman)
type: Item
instance of: scholarly article
title: Über eine Bemerkung von Glauberman. (On a remark of Glauberman)
zbMATH Open document ID: 0636.20015
DOI: 10.1007/BF01271656
author: Saad Adnan
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: The main result of this paper is: Theorem. Let G be a finite group such that \(N_ G(P)\) has a normal p-complement for some (and hence every) Sylow p-subgroup P of G for all primes p. Then G is nilpotent. - This Theorem generalizes a remark of Glauberman to the effect that a finite group G such that \(N_ G(P)=P\) for all Sylow p-subgroups P and all \(p\in \pi (G)\) must satisfy \(| \pi (G)| =1\). The first step in the proof of the Theorem applies two fundamental results to conclude that G has a normal subgroup of index p for some prime p.
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 4036058
zbMATH Keywords: finite group
zbMATH Keywords: normal p-complement
zbMATH Keywords: Sylow p-subgroup
zbMATH Keywords: nilpotent
reviewed by: Morton E. Harris
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4036058