Maximal subgroups in torsion branch groups
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929533760831488 |
|---|---|
| author | Garciarena, Mikel Eguzki Petschick, J. Moritz |
| author_facet | Garciarena, Mikel Eguzki Petschick, J. Moritz |
| contents | We study the maximal subgroups of branch groups and obtain a criterion that ensures that certain spinal groups are contained in the class $\mathcal{MF}$ of groups with all maximal subgroups of finite index. This allows us to construct branch groups within $\mathcal{MF}$ exhibiting novel properties, for example groups that possess non-normal maximal subgroups. Furthermore, we give new concrete examples of branch groups outside $\mathcal{MF}$, with explicitly given maximal subgroups of infinite index. Most prominently, we construct a periodic branch group outside $\mathcal{MF}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal subgroups in torsion branch groups Garciarena, Mikel Eguzki Petschick, J. Moritz Group Theory 20E08, 20E28 (Primary) 20F50 (Secondary) We study the maximal subgroups of branch groups and obtain a criterion that ensures that certain spinal groups are contained in the class $\mathcal{MF}$ of groups with all maximal subgroups of finite index. This allows us to construct branch groups within $\mathcal{MF}$ exhibiting novel properties, for example groups that possess non-normal maximal subgroups. Furthermore, we give new concrete examples of branch groups outside $\mathcal{MF}$, with explicitly given maximal subgroups of infinite index. Most prominently, we construct a periodic branch group outside $\mathcal{MF}$. |
| title | Maximal subgroups in torsion branch groups |
| topic | Group Theory 20E08, 20E28 (Primary) 20F50 (Secondary) |
| url | https://arxiv.org/abs/2410.06783 |