On $2$-closed abelian permutation groups

Dmitry Churikov; Ilia Ponomarenko

On $2$-closed abelian permutation groups

Group Theory 2020-11-25 v1 Combinatorics

Authors: Dmitry Churikov , Ilia Ponomarenko

Abstract

A permutation group $G\le\operatorname{Sym}(\Omega)$ is said to be $2$ -closed if no group $H$ such that $G<H\le\operatorname{Sym}(\Omega)$ has the same orbits on $\Omega\times\Omega$ as $G$ . A simple and efficient inductive criterion for the $2$ -closedness is established for abelian permutation groups with cyclic transitive constituents.

Keywords

permutation groups abelian groups nilpotent orbits

Cite

@article{arxiv.2011.12011,
  title  = {On $2$-closed abelian permutation groups},
  author = {Dmitry Churikov and Ilia Ponomarenko},
  journal= {arXiv preprint arXiv:2011.12011},
  year   = {2020}
}

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