On the upper exponent of a finite p-group

Let p be a prime and for a finite p-group G let (0)(G)=G and (i)(G)= 1( (i−1)(G)) for . A theorem is proved stating that, if exp(G)=q> and cl(G)=c, then the length of the (i)-series cannot be bounded by a function of q alone; an upper bound in terms of q and c is given which is shown to be attained in p-groups of arbitrarily large class.