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The growth of certain amalgamated free products and HNN-extensions

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

M. Edjvet  and
D. L. Johnson
M. Edjvet
Affiliation:
University of NottinghamUniversity Park Nottingham NG7 2RDU.K.
D. L. Johnson
Affiliation:
University of NottinghamUniversity Park Nottingham NG7 2RDU.K.
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Abstract

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Here we mean growth in the sense of Milnor and Gromov. After a brief survey of known results, we compute the growth series of the groups , with respect to generators {x, y}. This is done using minimal normal forms obtained by informal use of judiciously chosen rewrite rules. In both of these examples the growth series is a rational function, and we suspect that this is not the case for the Baumslag-Solitar group

.

MSC classification

Secondary: 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 3 , June 1992 , pp. 285 - 298
Copyright
Copyright © Australian Mathematical Society 1992

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