Vol. 35, No. 2, 1970

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On the number of finitely generated O-groups

Douglas B. Smith

Vol. 35 (1970), No. 2, 499–502

Let K be a class of relational systems of a fixed similarity type, n an infinite cardinal. A system A of cardinality n is (n,K)-weakly universal if each system in K of cardinality at most n is isomorphically embeddable in A. The object of this note is to construct 20 nonisomorphic finitely generated 0-groups and hence answer in the negative the following problem attributed to B. H. Neumann. Is there a group which is (0,K1)-weakly universal, where K1 is the class of O-groups?

Mathematical Subject Classification
Primary: 06.75
Received: 4 December 1969
Published: 1 November 1970
Douglas B. Smith