On the Tits alternative for cyclically presented groups with length-four positive relators-Reference-Cited by-同舟云学术

On the Tits alternative for cyclically presented groups with length-four positive relators

Published:2022-03-08 Issue:0 Volume:0 Page:
ISSN:1433-5883
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Isherwood Shaun¹,Williams Gerald¹^ORCID

Affiliation:

1. Department of Mathematical Sciences , University of Essex , Colchester , United Kingdom

Abstract

Abstract We investigate the Tits alternative for cyclically presented groups with length-four positive relators in terms of a system of congruences (A), (B), (C) in the defining parameters, introduced by Bogley and Parker. Except for the case when (B) holds and neither (A) nor (C) hold, we show that the Tits alternative is satisfied; in the remaining case, we show that the Tits alternative is satisfied when the number of generators of the cyclic presentation is at most 20.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2021-0131/pdf

Reference24 articles.

1. G. Baumslag, J. W. Morgan and P. B. Shalen, Generalized triangle groups, Math. Proc. Cambridge Philos. Soc. 102 (1987), no. 1, 25–31.

2. W. A. Bogley, On shift dynamics for cyclically presented groups, J. Algebra 418 (2014), 154–173.

3. W. A. Bogley and F. W. Parker, Cyclically presented groups with length four positive relators, J. Group Theory 21 (2018), no. 5, 911–947.

4. W. A. Bogley and G. Williams, Coherence, subgroup separability, and metacyclic structures for a class of cyclically presented groups, J. Algebra 480 (2017), 266–297.

5. W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), no. 3–4, 235–265.

Cited by 1 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. Redundant relators in cyclic presentations of groups;Journal of Group Theory;2023-06-22