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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cyclically presented groups embedded in one-relator products of cyclic groups


Authors: Colin M. Campbell, Patricia M. Heggie, Edmund F. Robertson and Richard M. Thomas
Journal: Proc. Amer. Math. Soc. 118 (1993), 401-408
MSC: Primary 20F05
MathSciNet review: 1140665
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Abstract: We consider the groups defined by the presentations

$\displaystyle \langle a,b:{a^2} = {b^n} = a{b^{ - 1}}ab{(aba{b^{ - 1}})^{\alpha - 1}}a{b^2}a{b^{ - 2}} = 1\rangle $

and investigate their structure for small values of $ \alpha $. This forms part of a general investigation into the structure of groups defined by presentations of the form

$\displaystyle \langle a,b:{a^2} = {b^n} = w(a,b) = 1\rangle .$

Connections between these groups and the Fibonacci groups are also explored.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1140665-9
PII: S 0002-9939(1993)1140665-9
Keywords: Cyclically presented, one-relator product, Fibonacci
Article copyright: © Copyright 1993 American Mathematical Society