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The growth series of compact hyperbolic Coxeter groups with 4 and 5 generators

  Published:1998-06-01
 Printed: Jun 1998
  • R. L. Worthington
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Abstract

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.
MSC Classifications: 20F05, 20F55 show english descriptions Generators, relations, and presentations
Reflection and Coxeter groups [See also 22E40, 51F15]
20F05 - Generators, relations, and presentations
20F55 - Reflection and Coxeter groups [See also 22E40, 51F15]
 

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