Vol. 35, No. 2, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
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