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On Nilpotent Products of Cyclic Groups. II

Published online by Cambridge University Press:  20 November 2018

Ruth Rebekka Struik
Ruth Rebekka Struik*
Affiliation:
University of British Columbia
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In a previous paper (18), G = F/Fn was studied for F a free product of a finite number of cyclic groups, and Fn 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 pαi, p a prime, αi positive integers, and n = 4, 5, … , p + 1.

(b) F a free product of cyclic groups of order 2αi, and n = 4.

In this paper, the following case is completely treated:

(c) F a free product of cyclic groups of order pαi p a prime, αi 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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 557 - 568
Copyright
Copyright © Canadian Mathematical Society 1961

References

16. Hall, Marshall, The theory of groups, Macmillan Co. (New York, 1959).Google Scholar
17. Ore, Oystein, Number theory and its history, McGraw-Hill Book Co., Inc. (New York, 1948).Google Scholar
18. Struik, R. R., On nilpotent products of cyclic groups, Can. J. Math., 12 (1960), 447–462.Google Scholar