Presentations of groups with even length relations
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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.
Webster , I 2021 , ' Presentations of groups with even length relations ' , Communications in Algebra , vol. Latest Articles . https://doi.org/10.1080/00927872.2021.1955903
Communications in Algebra
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.