J Austral Math Soc Ser A 52 pp285--298, 1992.

The Growth of Certain Amalgamated Free Products and HNN-Extensions

M. Edjvet

(Received 23 March 1990; revised 3 August 1990)

Abstract

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

áx, y | y^-1x^py = x^pñ and áx, y | x^p = y^pñ, p ³ 2

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

áx, y | y^-1x²y = x³ñ.

1991 AMS Subject Classification: 20E06

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Authors

M. Edjvet
D. L. Johnson: University of Nottingham, University Park, Nottingham NG7 2RD, U.K.

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Last Modified: Mon Feb 3 9:46:11 2003