Regular orbits of finite primitive solvable groups, the final classification

Derek Holt; Yong Yang

Regular orbits of finite primitive solvable groups, the final classification

Group Theory 2021-12-15 v1

Authors: Derek Holt , Yong Yang

Abstract

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.

Keywords

nilpotent orbits finite group theory permutation groups

Cite

@article{arxiv.2112.07505,
  title  = {Regular orbits of finite primitive solvable groups, the final classification},
  author = {Derek Holt and Yong Yang},
  journal= {arXiv preprint arXiv:2112.07505},
  year   = {2021}
}

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