# Finiteness properties for relatives of braided Higman--Thompson groups

@inproceedings{Skipper2021FinitenessPF, title={Finiteness properties for relatives of braided Higman--Thompson groups}, author={Rachel Skipper and Xiaolei Wu}, year={2021} }

We study the finiteness properties of the braided Higman–Thompson group bVd,r(H) with labels in H ≤ Bd, and bFd,r(H) and bTd,r(H) with labels in H ≤ PBd where Bd is the braid group with d strings and PBd is its pure braid subgroup. We show that for all d ≥ 2 and r ≥ 1, the group bVd,r(H) (resp. bTd,r(H) or bFd,r(H)) is of type Fn if and only if H is. Our result in particular confirms a recent conjecture of Aroca and Cumplido.

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