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arXiv · 2107.04783

The closures of wreath products in product action

I. Ponomarenko·A. V. Vasil'ev
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Abstract

Let $m$ be a positive integer and let $Ω$ be a finite set. The $m$-closure of $G\le$Sym$(Ω)$ is the largest permutation group on $Ω$ having the same orbits as $G$ in its induced action on the Cartesian product $Ω^m$. The exact formula for the $m$-closure of the wreath product in product action is given. As a corollary, a sufficient condition is obtained for this $m$-closure to be included in the wreath product of the $m$-closures of the factors.

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I. Ponomarenko, A. V. Vasil'ev. 2021-07-10. The closures of wreath products in product action. https://arxiv.org/abs/2107.04783

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