Capability of nilpotent products of cyclic groups II

Abstract

In Part I it was shown that if G is a p-group of class k, generated by elements of orders 1<p^{alpha_1} <= ... <= p^{alpha_r}, then a necessary condition for the capability of G is that r>1 and alpha_r <= alpha_{r-1} + [(k-1)/(p-1)]. It was also shown that when G is the k-nilpotent product of the cyclic groups generated by those elements and k=p=2 or k<p, then the given conditions are also sufficient. We make a correction related to the small class case, and extend the sufficiency result to k=p for arbitrary prime p.