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On Rationality of the Cogrowth Series

Author(s): Dmitri Kouksov
Journal: Proc. Amer. Math. Soc. 126 (1998), 2845-2847.
MSC (1991): Primary 20F05, 20P05, 05C38
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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: 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
Copyright of article: Copyright 1998, American Mathematical Society

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