Presentations of groups with even length relations

Isobel Webster

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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 languageEnglish
Number of pages8
JournalCommunications in Algebra
VolumeLatest Articles
Early online date15 Aug 2021
DOIs
Publication statusE-pub ahead of print - 15 Aug 2021

Keywords

  • Group presentations
  • Reflection groups
  • Cluster algebras
  • Parabolic subgroups

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