The closures of wreath products in product action

DOI10.1007/S10469-021-09640-0arXiv2107.04783MaRDI QIDQ6372463

I. N. Ponomarenko, Andrey V. Vasilev

Publication date: 10 July 2021

Abstract: Let $m$ be a positive integer and let $Omega$ be a finite set. The $m$-closure of $Gle$Sym$(Omega)$ is the largest permutation group on $Omega$ having the same orbits as $G$ in its induced action on the Cartesian product $Omeg{a}^m$. 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.

Mathematics Subject Classification ID

Extensions, wreath products, and other compositions of groups (20E22) Subgroups of symmetric groups (20B35)

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