Actions with nilpotent fixed point subgroup
type: Item
instance of: scholarly article
title: Actions with nilpotent fixed point subgroup
zbMATH Open document ID: 0917.20005
published in: Archiv der Mathematik
publication date: 1999-08-03T00:00:00Z
review text: The following results are proved: Theorems A+B+C. Suppose that \(A\) acts coprime on \(G\) (i.e., \((| A|,| G|)=1\)). (A+C) If \(C_G(A)\) normalizes every \(A\)-invariant Sylow subgroup of \(G\), then it also normalizes every maximal \(A\)-invariant subgroup of \(G\) and every \(A\)-invariant irreducible character of \(G\) is fully factorable. (B) If \(C_G(A)\) is nilpotent, then \(G\) is solvable. Note that \(\chi\in\text{Irr}(G)\) if, for every prime \(p\), \(\chi=\alpha_p\alpha_{p'}\), where \(\alpha_p\) and \(\alpha_{p'}\) are \(p\)-special and \(p'\)-special characters of \(G\), respectively.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D45
zbMATH DE Number: 1145740
zbMATH Keywords: \(p\)-special characters
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: maximal invariant subgroups
zbMATH Keywords: irreducible characters
author: Antonio Beltrán
reviewed by: Yakov Berkovich
MaRDI profile type: Publication
full work available at URL: s000130050107
OpenAlex ID: W128043982
DOI: 10.1007/S000130050107
description: scientific article; zbMATH DE number 1145740