Alexei A. Davydov Department of mathematics and mechanics, Moscow state University, Moscow, Russia. "Periodic lambda-rings" abstract: $\lambda$-ring is called $n$-periodic if its Adams operators satisfies to the following property: $\psi^{i+n}\ = \psi^i$ for any $i$. The free periodic $\lambda$-ring generated by one object is described. From this describtion one can deduce that the order of finite group devides the period in the power of dimension of faithful irreducible representation. Preprint