Regular orbits of finite primitive solvable groups, the final classification

Suppose that a finite solvable group G acts faithfully, irreducibly and quasi-primitively on a finite vector space V, and G is not metacyclic. Then G always has a regular orbit on V except for a few “small” cases. We completely classify these cases in this paper.

Saved in:
Bibliographic Details
Published in:Journal of symbolic computation 2023-05, Vol.116, p.139-145
Main Authors: Holt, Derek, Yang, Yong
Format: Article
Language:English
Subjects:
Primitive
Regular orbits
Solvable linear groups
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Suppose that a finite solvable group G acts faithfully, irreducibly and quasi-primitively on a finite vector space V, and G is not metacyclic. Then G always has a regular orbit on V except for a few “small” cases. We completely classify these cases in this paper.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2022.08.019