A note on higher coherence of graphs of groups

Abstract

Abstract For n ∈ N n\in\mathbb{N} , a group is called 𝑛-coherent if every subgroup of type F n \mathsf{F}_{n} is of type F n + 1 \mathsf{F}_{n+1} . For n ≥ 1 n\geq 1 , we observe that graphs of groups with 𝑛-coherent vertex groups and virtually poly-cyclic edge groups are 𝑛-coherent. We deduce the 𝑛-coherence of certain right-angled Artin groups.