Large orbits of odd-order subgroups of solvable linear groups.
type: Item
instance of: scholarly article
title: Large orbits of odd-order subgroups of solvable linear groups.
zbMATH Open document ID: 1252.20008
author: Yong Yang
published in: Journal of Algebra
publication date: 2012-06-18T00:00:00Z
review text: Let \(G\) be a finite solvable group and \(V\) a finite, faithful, completely reducible \(G\)-module. If \(H\) is an odd-order subgroup of \(G\), then \(H\) has at least two regular orbits on \(V\oplus V\). If, in addition \(|V|\) is odd, then there exists \(v\in V\) such that \(C_H(v)\subseteq F_2(G)\) (Theorem 1.2). Assume that, under the same hypotheses, \(V\) is endowed with a nonsingular symplectic form fixed by \(G\), then \(H\) has at least two regular orbits on \(V\) (Theorem 1.3).
reviewed by: Enrico Jabara
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 6046974
zbMATH Keywords: representations of solvable groups
zbMATH Keywords: solvable linear groups
zbMATH Keywords: regular orbits
zbMATH Keywords: odd order subgroups
zbMATH Keywords: completely reducible modules
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2011.10.016
OpenAlex ID: W2004433135
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DOI: 10.1016/J.JALGEBRA.2011.10.016
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description: scientific article; zbMATH DE number 6046974