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This article is cited in 3 scientific papers (total in 3 papers)
The closures of wreath products in product action
A. V. Vasilevab, I. N. Ponomarenkocb a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Abstract:
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, Pierce decomposition, $(1,1)$-superalgebra.
Received: 20.07.2021 Revised: 18.10.2021
Citation:
A. V. Vasilev, I. N. Ponomarenko, “The closures of wreath products in product action”, Algebra Logika, 60:3 (2021), 286–297; Algebra and Logic, 60:3 (2021), 188–195
Linking options:
https://www.mathnet.ru/eng/al2663 https://www.mathnet.ru/eng/al/v60/i3/p286
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Abstract page: | 204 | Full-text PDF : | 33 | References: | 31 | First page: | 5 |
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