The existence of regular orbits
type: Item
instance of: scholarly article
title: The existence of regular orbits
zbMATH Open document ID: 0654.20003
DOI: 10.1016/0021-8693(89)90251-2
author: Alberto Espuelas
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let G be a solvable group and p an odd prime. It is shown that if A is a p-subgroup of G and X is a p-chief factor of G on which A acts faithfully, then X contains a regular A-orbit, i.e., there exists \(x\in X\) such that \(C_ A(x)=1\). The result is false for \(p=2\). As a corollary, the following character-theoretic result is obtained: Let G be a solvable primitive group. Assume that F(G) is a p-group, p odd. Take \(P\in S_ p(G).Then\) \(b(P)=\max \{\psi (1)|\) \(\psi \in Irr(P)\}=| G:F(G)|_ p\).
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 4067171
zbMATH Keywords: solvable group
zbMATH Keywords: p-subgroup
zbMATH Keywords: p-chief factor
zbMATH Keywords: regular A-orbit
zbMATH Keywords: solvable primitive group
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90251-2
OpenAlex ID: W2004801300
cites work: Hall-Higman type theorems. V
cites work: Hall-Higman type theorems. VI
cites work: Q5187438
cites work: Finite groups with regular orbits on vector spaces
cites work: On the number of characters in a p-block of a p-solvable group
cites work: On the p -Length of p -Soluble Groups and Reduction Theorems for Burnside's Problem
cites work: The existence of regular orbits for nilpotent groups
cites work: Q3934684
cites work: The Influence of Nilpotent Subgroups on the Nilpotent Length and Derived Length of a Finite Group
cites work: Supersolvable automorphism groups of solvable groups.
description: scientific article; zbMATH DE number 4067171