Gruppi policiclici dotati di un automorfismo uniforme di ordine pq.

An automorphism ϕ of a group G is said to be uniform il for every g ∈ G there exists an h ∈ G such that g = h^−1h^ϕ . It is a well-known fact that if G is finite, an automorphism of G is uniform if and only if it is fixed-point-free. G. Zappa proved that if a polycyclic group G admits an uniform automorphism of prime order p then G is a finite (nilpotent) p -group. In this paper we continue Zappa’s work considering uniform automorphism of order pq (p and q distinct prime numbers). In particular we prove that there exists a constant μ (depending only on p and q) such that every torsion-free polycyclic group G admitting an uniform automorphism of order pq is nilpotent of class at most μ. As a consequence we prove that if a polycyclic group G admits an uniform automorphism of order pq then Zμ (G) has finite index in G.