Automorfismi involutori di $p$-gruppi finiti

Let p be a fixed odd prime number. In this note we study the class of finite p-groups G admitting an automorphism ϕ of order 2 such that G=< g^-1g^ϕ |g∈G〉 and (g^-1 g^ϕ )^p =1 for all g∈G. In this paper we prove that if the derived length of G is d and C G (ϕ) is nilpotent of class c, then the nilpotency class of G is bounded by a function depending only on d,c and p. We prove also that if p=3 and C G (ϕ) is nilpotent of class c, then G is nilpotent of class at most 2c+1