\(p\)-groups with a small number of character degrees and their normal subgroups
type: Item
instance of: scholarly article
title: \(p\)-groups with a small number of character degrees and their normal subgroups
author: Nabajit Talukdar
author: Kukil Kalpa Rajkhowa
published in: International Journal of Group Theory
publication date: 2024-11-28T00:00:00Z
review text: Assume that for any normal subgroup \(N\) of a finite \(p\)-group \(G\) either \(G'\leq N\) or \(N\leq \mathrm{Z}(G)\). The authors show that if \(|G/\mathrm{Z}(G)|=p^{2n+1}\), then \(cd(G)=\{1,p^n\}\). Moreover, they prove that if \(G\) is a finite \(p\)-group with nilpotency class not equal to \(3\), \(|G/\mathrm{Z}(G)|=p^{2n}\), and for any normal subgroup \(N\) of \(G\) either \(G'\leq N\) or \(|N\mathrm{Z}(G)/\mathrm{Z}(G)|\leq p\), then \(cd(G)\subseteq \{1,p^{n-1},p^n\}\).
reviewed by: S. M. Robati
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 7950848
zbMATH Keywords: character degrees
zbMATH Keywords: \(p\)-groups
zbMATH Keywords: nilpotency class
MaRDI profile type: Publication
DOI: 10.22108/IJGT.2024.141029.1897
description: scientific article; zbMATH DE number 7950848