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Peer-reviewedCC BYGroups Geometry and Dynamics

Rotation groups, mediangle graphs, and periagroups: A unified point of view on Coxeter groups and graph products of groups

  • Anthony Genevois1,2
  1. 1University of Montpellier, France
  2. 2Institut de Mathématiques de Marseille
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Abstract

In this article, we introduce rotation groups as a common generalisation of Coxeter groups and graph products of groups. We characterise these groups algebraically by presentations ( periagroups ), and we propose a combinatorial geometry ( mediangle graphs ) to study them. As an application, we give natural and unified proofs for several results that hold for both Coxeter groups and graph products of groups.

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Cite

BibTeXRIS
BibTeX
@article{genevois2026rotation,
  title = {{Rotation groups, mediangle graphs, and periagroups: A unified point of view on Coxeter groups and graph products of groups}},
  author = {Anthony Genevois},
  journal = {Groups Geometry and Dynamics},
  year = {2026},
  month = sep,
  doi = {10.4171/ggd/968},
  url = {https://doi.org/10.4171/ggd/968},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Rotation groups, mediangle graphs, and periagroups: A unified point of view on Coxeter groups and graph products of groups
AU  - Anthony Genevois
PY  - 2026
DA  - 2026/09/24
JO  - Groups Geometry and Dynamics
DO  - 10.4171/ggd/968
UR  - https://doi.org/10.4171/ggd/968
AB  - In this article, we introduce rotation groups as a common generalisation of Coxeter groups and graph products of groups. We characterise these groups algebraically by presentations ( periagroups ), and we propose a combinatorial geometry ( mediangle graphs ) to study them. As an application, we give natural and unified proofs for several results that hold for both Coxeter groups and graph products of groups.
SN  - 1661-7207
SN  - 1661-7215
ER  -