Geodesic
On profinite polyadic groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 814-823

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We study the structure of profinite polyadic groups and we prove that a polyadic topological group $(G, f)$ is profinite, if and only if, it is compact, Hausdorff, totally disconnected. More generally, for a pseudo-variety (or a formation) of finite groups $\mathfrak{X}$, we define the class of $\mathfrak{X}$-polyadic groups, and we show that a polyadic group $(G, f)$ is pro-$\mathfrak{X}$, if and only if, it is compact, Hausdorff, totally disconnected and for every open congruence $R$, the quotient $(G/R, f_R)$ is $\mathfrak{X}$-polyadic.
Keywords: Polyadic groups, $n$-ary groups, Profinite groups and polyadic groups, Post's cover and retract of a polyadic group. 
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M. Shahryari; M. Rostami. On profinite polyadic groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 814-823. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a5/