5 papers · 1 filter
Parabolic subgroups of Dyer groups
María Cumplido, Marina Salamero, Giovanni Sartori +1
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 conjugatin…
Dyer groups: Centres, hyperbolicity, and acylindrical hyperbolicity
Mireille Soergel, Nicolas Vaskou
In this article we describe the centres of all Dyer groups. We also give a complete classification of when a Dyer group is hyperbolic or acylindricality hyperbolic, with con…
Word problem and parabolic subgroups in Dyer groups
Luis Paris, Mireille Soergel
One can observe that Coxeter groups and right-angled Artin groups share the same solution to the word problem. On the other hand, in his study of reflection subgroups of Coxeter gr…
A generalization of the Davis-Moussong complex for Dyer groups
Mireille Soergel
A common feature of Coxeter groups and right-angled Artin groups is their solution to the word problem. Matthew Dyer introduced a class of groups, which we call Dyer groups, sharin…
Systolic complexes and group presentations
Mireille Soergel
We give conditions on a presentation of a group, which imply that its Cayley complex is simplicial and the flag complex of the Cayley complex is systolic. We then apply this to Gar…