DOI: 10.1515/jgth-2025-0187 ISSN: 1433-5883
A note on higher coherence of graphs of groups
Kevin Li, Luis Jorge Sánchez Saldaña 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.