Zeros of characters and the Frattini subgroup
type: Item
instance of: scholarly article
title: Zeros of characters and the Frattini subgroup
zbMATH Open document ID: 0711.20006
published in: Elemente der Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/141485
review text: The author proves the following theorem: Let G be a finite group with \(1<Z(G)<G\), Z(G) the center of G, and assume G has an irreducible non- linear character \(\chi\) such that A(\(\chi\)) contains fewer than \(| Z(G)|\) conjugate classes of elements where \(A(\chi)=\{g\in G|\chi (g)=0\}\). Then the Frattini subgroup \(\Phi\) (G)\(\neq 1\).
reviewed by: B.G.Basmaji
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 4168927
zbMATH Keywords: finite group
zbMATH Keywords: center
zbMATH Keywords: irreducible non-linear character
zbMATH Keywords: Frattini subgroup
author: Marian Deaconescu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4168927