Geodesic
On variety $\mathcal{N}$ of normal valued $m$-groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 54-60 Cet article a éte moissonné depuis la source Math-Net.Ru

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Recall that an $m$-group is a pair $(G,_{*}),$ where $G$ is an $\ell$-group and $_{*}$ is a decreasing order two automorphism of $G$. An $m$-group can be regarded as an algebraic system of signature $m$ and it is obvious that the $m$-groups form a variety in this signature. The set $M$ of varieties of all $m$-groups is a partially ordered set with respect to the set-theoretic inclusion. Moreover, $M$ is a lattice with respect to the naturally defined operations of intersection and union of varieties of $m$-groups. In this article we study the characteristics of a variety $\mathcal{N}$ of normal valued $m$-groups which is defined by the identity $ |x||y|\wedge |y|^{2}|x|^{2}=|x||y|.$ We will prove that $\mathcal{N}$ is an idempotent of $M$ and $\mathcal{N}=\bigvee\limits_{n \in \mathbb{N}}\mathcal{A}^{n},$ where $\mathcal{A}$ is the variety of all abelian $m$-groups.
Keywords: variety, normal valued $m$-group.
Mots-clés : $m$-group 
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A. V. Zenkov; O. V. Isaeva. On variety $\mathcal{N}$ of normal valued $m$-groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 54-60. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a0/

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