Characteristic Subgroup Growth
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911192290689024 |
|---|---|
| author | Hanany, Liam Lubotzky, Alexander |
| author_facet | Hanany, Liam Lubotzky, Alexander |
| contents | Let $s_n^\mathrm{ch}(Γ)$ denote the number of characteristic subgroups of index at most $n$ in a finitely generated group $Γ$. In response to a question of I. Rivin we show that if $Γ= F_r$ is the free group on $r \geq 2$ generators then the growth type of $s_n^{\mathrm{ch}}(F_r)$ is $n^{\mathrm{log}(n)}$. This is in contrast with the expectation of W. Thurston who predicted that there should be a difference between $r = 2$ and $r > 2$. Along the way we answer a question of arXiv:1703.07866 on the normal subgroup growth of large groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04150 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characteristic Subgroup Growth Hanany, Liam Lubotzky, Alexander Group Theory math.GR Let $s_n^\mathrm{ch}(Γ)$ denote the number of characteristic subgroups of index at most $n$ in a finitely generated group $Γ$. In response to a question of I. Rivin we show that if $Γ= F_r$ is the free group on $r \geq 2$ generators then the growth type of $s_n^{\mathrm{ch}}(F_r)$ is $n^{\mathrm{log}(n)}$. This is in contrast with the expectation of W. Thurston who predicted that there should be a difference between $r = 2$ and $r > 2$. Along the way we answer a question of arXiv:1703.07866 on the normal subgroup growth of large groups. |
| title | Characteristic Subgroup Growth |
| topic | Group Theory math.GR |
| url | https://arxiv.org/abs/2510.04150 |