On rationality of the cogrowth series-Reference-Cited by-同舟云学术

On rationality of the cogrowth series

Published:1998 Issue:10 Volume:126 Page:2845-2847
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Kouksov Dmitri

Abstract

The cogrowth series of a group G 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 G is finite. Except for the trivial group, this property is independent of presentation.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1998-126-10/S0002-9939-98-04741-8/S0002-9939-98-04741-8.pdf

Reference7 articles.

1. Cogrowth and amenability of discrete groups;Cohen, Joel M.;J. Funct. Anal.,1982

2. Symmetrical random walks on discrete groups;Grigorchuk, R. I.,1980

3. Cogrowth of groups and the Dedekind-Frobenius group determinant;Humphries, Stephen P.;Math. Proc. Cambridge Philos. Soc.,1997

4. Symmetric random walks on groups;Kesten, Harry;Trans. Amer. Math. Soc.,1959

5. EATCS Monographs on Theoretical Computer Science;Kuich, Werner,1986

Cited by 13 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Cogrowth series for free products of finite groups;International Journal of Algebra and Computation;2023-01-14

2. Finitely generated subgroups of free groups as formal languages and their cogrowth;journal of Groups, complexity, cryptology;2021-11-16

3. On the complexity of the cogrowth sequence;Journal of Combinatorial Algebra;2020-03-09

4. On Cogrowth, Amenability, and the Spectral Radius of a Random Walk on a Semigroup;International Mathematics Research Notices;2018-06-13

5. Sub-dominant Cogrowth Behavior and the Viability of Deciding Amenability Numerically;Experimental Mathematics;2017-08-22