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.
Categories: math.GR