On the Structure of Pro nite Polyadic Groups

We introduce pro nite polyadic groups as the n-ary generaliza- tions of a the ordinary pro nite groups. The structure of such pro nite sys- tems will be investigated and we will show that a topological polyadic group (G; f) is pro nite, if and only if, it is compact, Hausdor , totally discon- nected. It is also shown that a topological polyadic group der ;b(G; ) is pro nite, if and only if, the corresponding retract group (G; ) is pro nite and the automorphism is continuous. Also, for a variety (formation) X of nite polyadic groups, we show that a polyadic group (G; f) is pro-X, if and only if it is compact, Hausdor , totally disconnected and for every open congruence R, the nite polyadic group (G=R; fR) belongs to X.