On Nilpotent Products of Cyclic Groups. II

Abstract

In a previous paper (18), G = F/F n was studied for F a free product of a finite number of cyclic groups, and F n the normal subgroup generated by commutators of weight n . In that paper the following cases were completely treated: (a) F a free product of cyclic groups of order p α i , p a prime, α i positive integers, and n = 4, 5, … , p + 1. (b) F a free product of cyclic groups of order 2 α i , and n = 4. In this paper, the following case is completely treated: (c) F a free product of cyclic groups of order p α i p a prime, α i positive integers, and n = p + 2. (Note that n = 2 is well known, and n — 3 was studied by Golovin (2).) By ‘'completely treated” is meant: a unique representation of elements of the group is given, and the order of the group is indicated. In the case of n = 4, a multiplication table was given.