Über eine Bemerkung von Glauberman. (On a remark of Glauberman)
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.
scientific article; zbMATH DE number 4036058