Presentations of groups with even length relations
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.
Citation
Webster , I 2021 , ' Presentations of groups with even length relations ' , Communications in Algebra , vol. Latest Articles . https://doi.org/10.1080/00927872.2021.1955903
Publication
Communications in Algebra
Status
Peer reviewed
ISSN
0092-7872Type
Journal article
Rights
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.
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.