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arXiv · 2011.12011

On $2$-closed abelian permutation groups

Dmitry Churikov·Ilia Ponomarenko
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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.

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Dmitry Churikov, Ilia Ponomarenko. 2020-11-24. On $2$-closed abelian permutation groups. https://arxiv.org/abs/2011.12011

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