Regular orbits on symplectic modules
type: Item
instance of: scholarly article
title: Regular orbits on symplectic modules
zbMATH Open document ID: 0654.20004
DOI: 10.1016/0021-8693(91)90188-E
author: Alberto Espuelas
published in: Journal of Algebra
publication date: 1991-01-01T00:00:00Z
review text: Let G be a group of odd order and let V be a faithful and completely reducible KG-module, char(K)\(\neq 2\). Assume that V is endowed with a non- singular symplectic form fixed by G. Then V contains a regular G-orbit, i.e. there exists \(v\in V\) such that \(C_ G(v)=1\). The result is false when \(| G|\) is even or \(char(K)=2\). Using this result, a very strong theorem of Hall-Higman type for groups of odd order is obtained.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 4067172
zbMATH Keywords: completely reducible KG-module
zbMATH Keywords: symplectic form
zbMATH Keywords: regular G-orbit
zbMATH Keywords: theorem of Hall-Higman type
zbMATH Keywords: groups of odd order
MaRDI profile type: Publication
cites work: Hall-Higman type theorems. VI
cites work: The existence of regular orbits
cites work: Finite groups with regular orbits on vector spaces
cites work: Trivial Set-Stabilizers in Finite Permutation Groups
cites work: On the number of characters in a p-block of a p-solvable group
cites work: The existence of regular orbits for nilpotent groups
cites work: Endliche Gruppen I
cites work: Q3934684
cites work: Characters of Solvable and Symplectic Groups
cites work: Supersolvable automorphism groups of solvable groups.
cites work: Fixed point free action with regular orbits.
cites work: Solvable and Nilpotent Subgroups of GL(n,qm)
description: scientific article; zbMATH DE number 4067172