On a Functional Equation with a Group Isotopy Property

The set of all solutions of functional equation $F_1(F_2(z;x);F_3(y;z))=F_4(F_5(x;y);x)$ on quasigroup operations of an arbitrary fixed set are found. The result implies W. Dudek's theorem [1], which presents the operation in a quasigroup satisfying the identity $xy\cdot x=zx\cdot yz$.