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On Rationality of the Cogrowth Series |
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| Authors: | Dmitri Kouksov |
| Affiliation: | Department of Mathematics, Brigham Young University, Provo, Utah 84602 |
| Abstract: | The cogrowth series of a group  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  is finite. Except for the trivial group, this property is independent of presentation. |
| Keywords: | Cogrowth of groups rational series |
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