Non-solvable torsion-free virtually solvable groups
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915322462732288 |
|---|---|
| author | Hillman, Jonathan A. |
| author_facet | Hillman, Jonathan A. |
| contents | There are perfect Bieberbach groups of Hirsch length 15, but none in lower dimensions. We shall show that a nonsolvable, torsion free, virtually solvable group $S$ must have Hirsch length $h(S)\geq10$. If $h(S)\leq13$ then we may assume that $A_5$ is the only simple factor, but $PSL(2,7)$ and $SL(2,8)$ may occur when $h(S)\geq14$. There are no known examples with $h(S)<15$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09513 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-solvable torsion-free virtually solvable groups Hillman, Jonathan A. Group Theory 20F19 There are perfect Bieberbach groups of Hirsch length 15, but none in lower dimensions. We shall show that a nonsolvable, torsion free, virtually solvable group $S$ must have Hirsch length $h(S)\geq10$. If $h(S)\leq13$ then we may assume that $A_5$ is the only simple factor, but $PSL(2,7)$ and $SL(2,8)$ may occur when $h(S)\geq14$. There are no known examples with $h(S)<15$. |
| title | Non-solvable torsion-free virtually solvable groups |
| topic | Group Theory 20F19 |
| url | https://arxiv.org/abs/2302.09513 |