Limit groups over coherent right-angled Artin groups
A new class of groups C, containing all coherent RAAGs and all toral relatively hyperbolic groups, is defined. It is shown that, for a group G in the class C, the Z[t]-exponential group GZ[t] may be constructed as an iterated centraliser extension. Using this fact, it is proved that GZ[t] is fully r...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:271768 |
| Acceso en línea: | https://ddd.uab.cat/record/271768 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6712305 |
| Access Level: | acceso abierto |
| Palabra clave: | Partially commutative group Right-angled artin group Limit group Hyperbolic group |
| Sumario: | A new class of groups C, containing all coherent RAAGs and all toral relatively hyperbolic groups, is defined. It is shown that, for a group G in the class C, the Z[t]-exponential group GZ[t] may be constructed as an iterated centraliser extension. Using this fact, it is proved that GZ[t] is fully residually G (i.e. it has the same universal theory as G) and so its finitely generated subgroups are limit groups over G. If G is a coherent RAAG, then the converse also holds - any limit group over G embeds into GZ[t]. Moreover, it is proved that limit groups over G are finitely presented, coherent and CAT(0), so in particular have solvable word and conjugacy problems. |
|---|