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

Campbell, Colin M.; Heggie, Patricia M.; Robertson, Edmund F.; Thomas, Richard M.

doi:10.1090/S0002-9939-1993-1140665-9

Cyclically presented groups embedded in one-relator products of cyclic groups
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by Colin M. Campbell, Patricia M. Heggie, Edmund F. Robertson and Richard M. Thomas PDF

Proc. Amer. Math. Soc. 118 (1993), 401-408 Request permission

Abstract:

We consider the groups defined by the presentations \[ \langle a,b:{a^2} = {b^n} = a{b^{ - 1}}ab{(aba{b^{ - 1}})^{\alpha - 1}}a{b^2}a{b^{ - 2}} = 1\rangle \] 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 \[ \langle a,b:{a^2} = {b^n} = w(a,b) = 1\rangle .\] Connections between these groups and the Fibonacci groups are also explored.

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