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math.GR2025
Minimal generating set of cactus groups
Eddy Godelle
We prove that the lower central series of the cactus group associated with a non commutative Coxeter group never stabilizes. We also compute a minimal presentation in terms of gene…
math.GR2024
Trickle groups
Paolo Bellingeri, Eddy Godelle, Luis Paris
A new family of groups, called trickle groups, is presented. These groups generalize right-angled Artin and Coxeter groups, as well as cactus groups. A trickle group is defined by…
math.GR2024
Retraction to a parabolic subgroup and applications
François Digne, Eddy Godelle, Jean Michel
We continue the study of the retraction from an Artin group to a standard parabolic subgroup introduced by Blufstein, Charney, Paris and the second author. Using right and left ret…