Regular orbits of self-dual modules
type: Item
instance of: scholarly article
title: Regular orbits of self-dual modules
zbMATH Open document ID: 1487.20006
author: Ping Jin
author: Yong Yang
published in: Archiv der Mathematik
publication date: 2021-06-09T00:00:00Z
review text: The authors prove that if $V$ is a faithful completely reducible self-dual $FG$-module for a finite solvable group $G$, where $F$ is a finite field of characteristic $p$, then if either $p$ is odd, or $p = 2$ and $|H|$ is not divisible by 3, then the subgroup $H$ of $G$ has at least two regular orbits on $V$. This improves earlier results of a similar nature by \textit{A. Espuelas} [J. Algebra 138, No. 1, 1--12 (1991; Zbl 0654.20004)] and by the second author [J. Algebra 351, No. 1, 220--234 (2012; Zbl 1252.20008)].
reviewed by: Geoffrey R. Robinson
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 7357042
zbMATH Keywords: regular orbit
zbMATH Keywords: group action
zbMATH Keywords: self-dual module
MaRDI profile type: Publication
full work available at URL: s00013-021-01577-1
OpenAlex ID: W3131183300
cites work: Regular orbits on symplectic modules
cites work: Q3934684
cites work: Self-dual modules for finite groups of odd order.
cites work: Q4273959
cites work: Q3826736
cites work: Large orbits of odd-order subgroups of solvable linear groups.
DOI: 10.1007/S00013-021-01577-1
description: scientific article; zbMATH DE number 7357042