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The Growth Series of Compact Hyperbolic Coxeter Groups with 4 and 5 Generators

Published online by Cambridge University Press:  20 November 2018

R. L. Worthington
R. L. Worthington*
Affiliation:
Department of Mathematics the University of Nottingham University Park Nottingham NG7 2RD England
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Abstract

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The growth series of compact hyperbolic Coxeter groups with 4 and 5 generators are explicitly calculated. The assertions of J. Cannon and Ph. Wagreich for the 4-generated groups, that the poles of the growth series lie on the unit circle, with the exception of a single real reciprocal pair of poles, are verified. We also verify that for the 5-generated groups, this phenomenon fails.

Keywords

20F0520F55
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 2 , 01 June 1998 , pp. 231 - 239
Copyright
Copyright © Canadian Mathematical Society 1998

References

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5. Albar, M. A., Al-Hamed, M. A. and Al-Saleh, N. A., The growth of Coxeter groups, preprint.Google Scholar