On the probability of satisfying a word in nilpotent groups of class 2
  Let G be a finite group of nilpotency class 2 and w a group word. In this short paper we show that the probability that a random n-tuple of elements from G satisfies w is at least one over the order of G. This answers a special case of a conjecture of Alon Amit. 
Matthew Levy
math.GR