Subgroups of Bestvina-Brady groups
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929699058352128 |
|---|---|
| author | Blumer, Simone |
| author_facet | Blumer, Simone |
| contents | In "Subgroups of Graph Groups", 1987, J. Alg., Droms proved that all the subgroups of a right-angled Artin group (RAAG) defined by a finite simplicial graph $Γ$ are themselves RAAGs if, and only if, $Γ$ has no induced square graph nor line-graph of length $3$. The present work provides a similar result for specific normal subgroups of RAAGs, called Bestvina-Brady groups: We characterize those graphs in which every subgroup of such a group is itself a RAAG. In turn, we confirm several Galois theoretic conjectures for the pro-$p$ completions of these groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subgroups of Bestvina-Brady groups Blumer, Simone Group Theory Combinatorics Rings and Algebras 20F65, 05C35, 17B56 In "Subgroups of Graph Groups", 1987, J. Alg., Droms proved that all the subgroups of a right-angled Artin group (RAAG) defined by a finite simplicial graph $Γ$ are themselves RAAGs if, and only if, $Γ$ has no induced square graph nor line-graph of length $3$. The present work provides a similar result for specific normal subgroups of RAAGs, called Bestvina-Brady groups: We characterize those graphs in which every subgroup of such a group is itself a RAAG. In turn, we confirm several Galois theoretic conjectures for the pro-$p$ completions of these groups. |
| title | Subgroups of Bestvina-Brady groups |
| topic | Group Theory Combinatorics Rings and Algebras 20F65, 05C35, 17B56 |
| url | https://arxiv.org/abs/2502.03215 |