Parabolic subgroups of Dyer groups

María Cumplido; Marina Salamero; Giovanni Sartori; Mireille Soergel

Parabolic subgroups of Dyer groups

Group Theory 2026-06-30 v1

Authors: María Cumplido , Marina Salamero , Giovanni Sartori , Mireille Soergel

Abstract

For all Dyer groups, we find an algorithm to determine when two parabolic subgroups are conjugate. Given two conjugate standard parabolic subgroup, we fully describe the conjugating elements in terms of ribbons, showing that the ribbon conjecture holds true. In particular we give a description of the normaliser of a parabolic subgroup using ribbons. We prove the standardisation property for parabolic subgroups and deduce that an arbitrary intersection of parabolic subgroups is a parabolic subgroup.

Cite

@article{arxiv.2607.00181,
  title  = {Parabolic subgroups of Dyer groups},
  author = {María Cumplido and Marina Salamero and Giovanni Sartori and Mireille Soergel},
  journal= {arXiv preprint arXiv:2607.00181},
  year   = {2026}
}

Comments

18 pages, 4 figures