Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On profinite polyadic groups   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.

13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex