Regular orbits of finite primitive solvable groups, III

Yong Yang; Alexey Vasil'ev; Evgeny Vdovin

Regular orbits of finite primitive solvable groups, III

Group Theory 2020-12-21 v2

Authors: Yong Yang , Alexey Vasil'ev , Evgeny Vdovin

Abstract

Suppose that a finite solvable group $G$ acts faithfully, irreducibly and quasi-primitively on a finite vector space $V$ . Then $G$ has a uniquely determined normal subgroup $E$ which is a direct product of extraspecial $p$ -groups for various $p$ and we denote $e=\sqrt{|E/\bZ(E)|}$ . We prove that when $e=2,3,4,8,9,16$ , $G$ will have regular orbits on $V$ when the corresponding vector space is not too small.

Keywords

nilpotent orbits permutation groups finite group theory

Cite

@article{arxiv.1612.05959,
  title  = {Regular orbits of finite primitive solvable groups, III},
  author = {Yong Yang and Alexey Vasil'ev and Evgeny Vdovin},
  journal= {arXiv preprint arXiv:1612.05959},
  year   = {2020}
}

Comments

arXiv admin note: text overlap with arXiv:1208.4022

Regular orbits of finite primitive solvable groups, III

Abstract

Keywords

Cite

Comments

Related papers