Presentations of groups with even length relations

Isobel Webster

doi:10.1080/00927872.2021.1955903

Presentations of groups with even length relations

Isobel Webster

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the properties of groups that have presentations in which the generating set is a fixed set of involutions and all additional relations are of even length. We consider the parabolic subgroups of such a group and show that every element has a factorization with respect to a given parabolic subgroup. Furthermore, we give a counterexample, using a cluster group presentation, which demonstrates that this factorization is not necessarily unique.

Original language	English
Number of pages	8
Journal	Communications in Algebra
Volume	Latest Articles
Early online date	15 Aug 2021
DOIs	https://doi.org/10.1080/00927872.2021.1955903
Publication status	E-pub ahead of print - 15 Aug 2021

Keywords

Group presentations
Reflection groups
Cluster algebras
Parabolic subgroups

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10.1080/00927872.2021.1955903Licence: CC BY-NC-ND

Webster_2021_CIA_Presentations-of-groups_CC
Copyright 2021 The Author(s). Published with license by Taylor and Francis Group, LLC. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
Final published version, 1.2 MBLicence: CC BY-NC-ND

Cite this

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AB - We study the properties of groups that have presentations in which the generating set is a fixed set of involutions and all additional relations are of even length. We consider the parabolic subgroups of such a group and show that every element has a factorization with respect to a given parabolic subgroup. Furthermore, we give a counterexample, using a cluster group presentation, which demonstrates that this factorization is not necessarily unique.

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KW - Cluster algebras

KW - Parabolic subgroups

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Presentations of groups with even length relations

Abstract

Keywords

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