Characterizations of \(p\)-nilpotent groups
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)].
scientific article; zbMATH DE number 639574