Character degrees of nilpotent-by-metacyclic groups
type: Item
instance of: scholarly article
title: Character degrees of nilpotent-by-metacyclic groups
zbMATH Open document ID: 0813.20006
author: Alberto Espuelas
published in: Journal of Algebra
publication date: 1994-06-07T00:00:00Z
review text: Let \(G\) be a finite solvable group and let \(\pi(n)\) be the set of prime divisors of an integer \(n\). Let \[ \rho(G) = \bigcup_{\chi \in \text{Irr}(G)} \pi(\chi(1)) \quad \text{and}\quad \sigma(G) = \max_{\chi\in \text{Irr}(G)} | \pi(\chi(1))|. \] A question of Huppert concerns the validity of the inequality \(| \rho(G)| \leq 2\sigma (G)\). Gluck and Manz have shown that this problem may be reduced to the nilpotent-by-metabelian case. The author proves that if \(G\) is nilpotent-by-metacyclic, then \(| \rho(G)| \leq 2 \sigma(G)\).
reviewed by: B.G.Basmaji
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 554237
zbMATH Keywords: irreducible character degrees
zbMATH Keywords: finite solvable group
zbMATH Keywords: nilpotent-by- metabelian
zbMATH Keywords: nilpotent-by-metacyclic
MaRDI profile type: Publication
full work available at URL: jabr.1993.1268
OpenAlex ID: W2042797989
DOI: 10.1006/JABR.1993.1268
Recommended article: Q4312076
Recommended article: The character degrees and nilpotence class of a \(p\)-group
Recommended article: Character degrees, character codegrees and nilpotence class of p-groups
Recommended article: Characters of nilpotent groups
Recommended article: A remark on character degrees and nilpotence class in \(p\)-groups.
Recommended article: Character degrees and nilpotence class of finite 𝑝-groups: An approach via pro-𝑝 groups
Recommended article: Characterisation of nilpotent-by-finite groups
Recommended article: A character theoretic condition characterizing nilpotent groups
Recommended article: Characterizations of \(p\)-nilpotent groups
Recommended article: Characterization of non-nilpotent groups with two irreducible character degrees.
description: scientific article; zbMATH DE number 554237