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A finitely generated, infinitely related group with trivial multiplicator

Published online by Cambridge University Press:  17 April 2009

Gilbert Baumslag
Gilbert Baumslag
Affiliation:
Rice University, Houston, Texas, USA.
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Abstract

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We exhibit a 3-generator metabelian group which is not finitely related but has a trivial multiplicator.

1. The purpose of this note is to establish the exitense of a finitely generated group which is not finitely related, but whose multiplecator is finitely generated. This settles negatively a question whichb has been open for a few years (it was first brought to my attention by Michel Kervaire and Joan Landman Dyer in 1964, but I believe it is somewhat older). The group is given in the follwing theorem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 1 , August 1971 , pp. 131 - 136
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Magnus, Wilhelm; Karrass, Abraham; Solitar, Donald, Combintorial group theory: Presentations of groups in terms of generators and relations (interscience ]John Wiley & Sons], New York, London, Sydney, 1966).Google Scholar
[2]Neumann, B.H., “Some remarks on infinite groups”, J. London Math. Soc. 12 (1937), 120–127.Google Scholar