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On the number of
finitely generated O-groups
Douglas B. Smith |
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Vol. 35 (1970), No. 2, 499–502
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Abstract |
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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 2ℵ0 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 (ℵ0,K1)-weakly universal, where K1 is the class of O-groups? |
Mathematical Subject Classification
Primary: 06.75
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Milestones
Received: 4 December 1969
Published: 1 November 1970
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Authors |
| Douglas B. Smith | |
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