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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Rationality of the Cogrowth Series


Author: Dmitri Kouksov
Journal: Proc. Amer. Math. Soc. 126 (1998), 2845-2847
MSC (1991): Primary 20F05, 20P05, 05C38
MathSciNet review: 1487319
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Abstract: The cogrowth series of a group $G$ depends on the presentation of the group. We show that the cogrowth series of a non-empty presentation is a rational function not equal to 1 if and only if $G$ is finite. Except for the trivial group, this property is independent of presentation.


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Additional Information

Dmitri Kouksov
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: dmitri@math.byu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04741-8
PII: S 0002-9939(98)04741-8
Keywords: Cogrowth of groups, rational series
Received by editor(s): March 13, 1997
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society