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arXiv · 2510.15462

Minimal generating set of cactus groups

Eddy Godelle
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Abstract

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 generators for the cactus group associated with a finite Coxeter groups, except in type E.

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Eddy Godelle. 2025-10-17. Minimal generating set of cactus groups. https://arxiv.org/abs/2510.15462

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