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Free products of locally indicable groups with a single relator

Published online by Cambridge University Press:  17 April 2009

Benjamin Baumslag
Benjamin Baumslag
Affiliation:
Department of Mathematics, Imperial College of Science & Technology, Queen's Gate, London SW7 2BZ, England
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Abstract

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The method of proof of Magnus introduced in 1930 is adapted to prove the following theorem of Howie. If A and B are groups for which every finitely generated subgroup has an infinite cyclic image, and if one adds an additional relation (with obvious exceptions), then in the resultant group both A and B appear isomorphically.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 3 , June 1984 , pp. 401 - 404
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Baumslag, B. and Pride, S.J., “An extension of the Freiheitsatz”, Math. Proc. Cambridge Phil. Soc. 89 (1981), 35–41.CrossRefGoogle Scholar
[2]Howie, J., “On pairs of 2-complexes and systems of equations over groups”, J. reine angewandte Math. 324 (1981), 165–174.Google Scholar
[3]Magnus, W., “Ueber diskontinuierliche Gruppen mit einer definierenden Relation (Der Freiheitsatz)”, J. reine angew. Math. 163 (1930), 141–165.CrossRefGoogle Scholar