Geodesic
The closures of wreath products in product action
Algebra i logika, Tome 60 (2021) no. 3, pp. 286-297.

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Let $m$ be a positive integer and let $\Omega$ be a finite set. The $m$-closure of $G\le{\rm Sym} (\Omega)$ is the largest permutation group $G^{(m)}$ on $\Omega$ having the same orbits as $G$ in its induced action on the Cartesian product $\Omega^m$. An 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.
Keywords: right-symmetric ring, left-symmetric algebra, pre-Lie algebra, prime ring, $(1,1)$-superalgebra.
Mots-clés : Pierce decomposition 
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A. V. Vasilev; I. N. Ponomarenko. The closures of wreath products in product action. Algebra i logika, Tome 60 (2021) no. 3, pp. 286-297. http://geodesic.mathdoc.fr/item/AL_2021_60_3_a1/

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