  Let G be a finite group, p a fixed prime and P a Sylow p-subgroup of G. In
this short note we prove that if p is odd, G is p-nilpotent if and only if P
controls fusion of cyclic groups of order p. For the case p=2, we show that G
is p-nilpotent if and only if P controls fusion of cyclic groups of order 2 and
4.
