Structure of $k$-closures of finite nilpotent permutation groups

Dmitry Churikov

Structure of $k$-closures of finite nilpotent permutation groups

Group Theory 2021-07-27 v1 Combinatorics

Authors: Dmitry Churikov

Abstract

Let $G$ be a permutation group on a set $\Omega$ , and $k$ a positive integer. The $k$ -closure $G^{(k)}$ of $G$ is the largest subgroup of $\operatorname{Sym}(\Omega)$ , with the same as $G$ orbits of componentwise action on $\Omega^k$ . We prove that the $k$ -closure of a finite nilpotent permutation group is the direct product of $k$ -closures of its Sylow subgroups.

Keywords

permutation group k-closure finite nilpotent group Sylow subgroups direct product

Cite

@article{arxiv.2107.11771,
  title  = {Structure of $k$-closures of finite nilpotent permutation groups},
  author = {Dmitry Churikov},
  journal= {arXiv preprint arXiv:2107.11771},
  year   = {2021}
}

Related papers

View all related →