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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{AL_2021_60_3_a1,
     author = {A. V. Vasilev and I. N. Ponomarenko},
     title = {The closures of wreath products in product action},
     journal = {Algebra i logika},
     pages = {286--297},
     publisher = {mathdoc},
     volume = {60},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_3_a1/}
}
TY  - JOUR
AU  - A. V. Vasilev
AU  - I. N. Ponomarenko
TI  - The closures of wreath products in product action
JO  - Algebra i logika
PY  - 2021
SP  - 286
EP  - 297
VL  - 60
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2021_60_3_a1/
LA  - ru
ID  - AL_2021_60_3_a1
ER  - 
%0 Journal Article
%A A. V. Vasilev
%A I. N. Ponomarenko
%T The closures of wreath products in product action
%J Algebra i logika
%D 2021
%P 286-297
%V 60
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2021_60_3_a1/
%G ru
%F AL_2021_60_3_a1
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/