On subgroup separability and membership problems in twisted right-angled Artin groups
Abstract
We characterize twisted right-angled Artin groups (T-RAAGs) that are subgroup separable using only their defining mixed graphs: such a group is subgroup separable if and only if the underlying simplicial graph contains no induced path or square on four vertices. This generalizes the results of Metaftsis and Raptis on classical right-angled Artin groups. We also show that the subgroup membership problem is decidable when the group is coherent—which occurs precisely when the defining mixed graph is chordal. Furthermore, we exhibit a family of cone-type mixed graphs for which the corresponding T-RAAGs have decidable rational and submonoid membership problems.
Fields of Study & Subjects
Geometric and Algebraic Topology
Finite Group Theory Research
Advanced Operator Algebra Research
Publication details
- Journal / source
- Communications in Algebra
- Volume
- 54
- Issue
- 9
- Pages
- 3189–3201
- Publication date
- 5 January 2026
- Language
- EN