on the structure of pronite polyadic groups

We introduce pronite polyadic groups as the n-ary generaliza-tions of a the ordinary pronite groups. the structure of such pronite sys-tems will be investigated and we will show that a topological polyadic group(g; f) is pronite, if and only if, it is compact, hausdor, totally discon-nected. it is also shown that a topological polyadic group der;b(g; ) ispronite, if and only if, the corresponding retract group (g; ) is proniteand the automorphism  is continuous. also, for a variety (formation) xof nite polyadic groups, we show that a polyadic group (g; f) is pro-x, ifand only if it is compact, hausdor, totally disconnected and for every opencongruence r, the nite polyadic group (g=r; fr) belongs to x.