Characterizations of \(p\)-nilpotent groups
type: Item
instance of: scholarly article
title: Characterizations of \(p\)-nilpotent groups
zbMATH Open document ID: 0833.20013
author: Masafumi Murai
published in: Osaka Journal of Mathematics
publication date: 1996-03-12T00:00:00Z
review text: Let \(G\) be a finite group and let \(p\) be a prime. The results in this paper are mainly concerned with characters of height 0 in the principal \(p\)-block and with implications for the \(p\)-nilpotency of \(G\). For example it is shown that \(G\) is \(p\)-nilpotent if and only if every character of height 0 in the principal block is modularly irreducible. Various significant normal subgroups are defined by characters and shown to be \(p\)-nilpotent. The paper ends with an equivalent characterisation of a criterion introduced by \textit{T. Ono} [Proc. Japan Acad., Ser. A 65, No. 8, 304-306 (1989; Zbl 0709.11062)].
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 639574
zbMATH Keywords: finite groups
zbMATH Keywords: characters of height 0
zbMATH Keywords: principal \(p\)-blocks
zbMATH Keywords: \(p\)- nilpotency
zbMATH Keywords: modularly irreducible characters
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 639574