Big primes and character values for solvable groups
type: Item
instance of: scholarly article
title: Big primes and character values for solvable groups
zbMATH Open document ID: 0587.20004
DOI: 10.1016/0021-8693(86)90079-7
author: Eliana Faris e Soares
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: It was shown by \textit{F. M. Markel} [ibid. 26, 69-74 (1973; Zbl 0274.20030)], that if the finite supersolvable group G has all its character values in \({\mathbb{Q}}\), then no prime bigger than 3 divides the order of G. This was extended by \textit{R. Gow} [ibid. 40, 280-299 (1976; Zbl 0348.20017)], who proved that for a finite solvable group G having all its character values in \({\mathbb{Q}}\), the order of G is not divisible by any prime bigger than 5. This work extends the above results in several directions. One of the main results is Theorem: Let G be a finite solvable group whose character values lie all in a field of degree n over \({\mathbb{Q}}\) and let p be a prime divisor of the order of G. Then \(p\leq 16n^ 2+1\). In fact, there are several theorems proved here in the same spirit.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 3941772
zbMATH Keywords: character values
zbMATH Keywords: finite solvable group
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90079-7
OpenAlex ID: W2112162190
cites work: Solvable and supersolvable groups in which every element is conjugate to its inverse
cites work: Groups whose characters are rational-valued
cites work: Q3856819
cites work: Endliche Gruppen I
cites work: Q4103728
cites work: Groups with many conjugate elements
cites work: p-solvable doubly transitive permutation groups
description: scientific article; zbMATH DE number 3941772