Actions and invariant character degrees. II
type: Item
instance of: scholarly article
title: Actions and invariant character degrees. II
zbMATH Open document ID: 0868.20004
author: Gabriel Navarro
published in: Journal of Algebra
publication date: 1996-11-13T00:00:00Z
review text: In part I [ibid. 160, No. 1, 172-178 (1993; Zbl 0805.20007)] the author gave evidence that there exists a rich and useful relationship between the \(A\)-stable structure of a finite group \(G\) on which \(A\) acts coprimely, and the set \(\text{cd}_A(G)\) of degrees of the complex irreducible \(A\)-invariant characters of \(G\). What can be said about the fixed-points subgroup \(C_G(A)\) if much is known about \(\text{cd}_A(G)\)? In this paper some theory is developed centering around the above theme. The following is the main outcome: Theorem A. Suppose that a finite group \(A\) acts coprimely on a finite supersolvable group \(G\). Then the derived length of \(C_G(A)\) is bounded by \(|\text{cd}_A(G)|\).
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D45
zbMATH DE Number: 930148
zbMATH Keywords: degrees of complex irreducible characters
zbMATH Keywords: finite groups
zbMATH Keywords: fixed-points subgroups
zbMATH Keywords: finite supersolvable groups
zbMATH Keywords: derived lengths
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
full work available at URL: jabr.1996.0266
OpenAlex ID: W4212870817
DOI: 10.1006/JABR.1996.0266
description: scientific article; zbMATH DE number 930148