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Some Group Presentations

Published online by Cambridge University Press:  20 November 2018

B. H. Neumann
B. H. Neumann*
Affiliation:
Institute of A dvanced Studies, Australian National University, Canberra, ACT, Australia Commonwealth Scientific and Industrial Research Organization, Canberra, A CT, Australia
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Extract

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Let the group be presented on three generators a, b, c with three defining relations

where p, q, r, s, t, u are integers, the “parameters” of the presentation.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 4 , 01 August 1978 , pp. 838 - 850
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Gilbert, Baumslag and Donald, Solitar, Some two-generator one-relator non-Hopfian groups, Bull. Amer. Math. Soc. 68 (1962), 199–201.Google Scholar
2. Graham, Higman, A finitely generated infinite simple group, J. London Math. Soc. 26 (1951), 61–64.Google Scholar
3. Neumann, B. H., An essay on free products of groups with amalgamations, Phil. Trans. Roy Soc. London Ser. A 2-6 (1954), 503–554.Google Scholar
4. Post, Michael J., A note on some finite three-generator groups with zero deficiency, to appear.Google Scholar
5. van der Waerden, B. L., Free products of groups, Amer. J. Math. 70 (1948), 527–528.Google Scholar