Periodic Endomorphisms of Polycyclic Groups

Let G be a polycyclic group. As a consequence of known results, any periodic group of automorphisms of G is finite and there is an upper bound (depending only on G) for its order. On the other hand, a periodic semigroup of endomorphisms of G need not be finite but we prove that it is locally finite. Also we show that the order of periodic endomorphisms of G is bounded.