On Nilpotent Products of Cyclic Groups
Ruth Rebekka Struik · Canadian Journal of Mathematics · 1960
In this paperG=F/Fnis studied forFa free product of a finite number of cyclic groups, andFnthe normal subgroup generated by commutators of weightn. The case ofn =4 is completely treated(F/F2is well known;F/F3is completely treated in (2)); special cases ofn >4 are studied; a partial conjecture is offered in regard to the unsolved cases. Forn= 4 a multiplication table and other properties are given. The problem arose from Golovin's work on nilpotent products ((1), (2), (3)) which are of interest because they are generalizations of the free and direct product of groups: all nilpotent groups are factor groups of nilpotent products in the same sense that all groups are factor groups of free products, and all Abelian groups are factor groups of direct products. In particular (as is well known) every finite Abelian group is a direct product of cyclic groups. Hence it becomes of interest to investigate nilpotent products of finite cyclic groups.