On Normal Subgroups of Twisted Chevalley Groups over Commutative Rings
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913960080441344 |
|---|---|
| author | Garge, Shripad M. Makadiya, Deep H. |
| author_facet | Garge, Shripad M. Makadiya, Deep H. |
| contents | In this paper, we prove two structure theorems for twisted Chevalley groups $G_σ(R)$ over a commutative ring $R$ with unity. The first theorem concerns the normality of $E'_σ(R,J)$, the elementary congruence subgroups at level $J$, in the group $G_σ(R)$. The second theorem classifies all subgroups of $G_σ(R)$ normalized by its elementary subgroup $E'_σ(R)$. Along the way, we obtain several interesting results. For instance, when $R$ is a semilocal ring, we show that $G_σ(R)$ can be expressed as the (internal) product of $E'_σ(R)$ and the maximal torus $T_σ(R)$ of $G_σ(R)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Normal Subgroups of Twisted Chevalley Groups over Commutative Rings Garge, Shripad M. Makadiya, Deep H. Group Theory 20G35 In this paper, we prove two structure theorems for twisted Chevalley groups $G_σ(R)$ over a commutative ring $R$ with unity. The first theorem concerns the normality of $E'_σ(R,J)$, the elementary congruence subgroups at level $J$, in the group $G_σ(R)$. The second theorem classifies all subgroups of $G_σ(R)$ normalized by its elementary subgroup $E'_σ(R)$. Along the way, we obtain several interesting results. For instance, when $R$ is a semilocal ring, we show that $G_σ(R)$ can be expressed as the (internal) product of $E'_σ(R)$ and the maximal torus $T_σ(R)$ of $G_σ(R)$. |
| title | On Normal Subgroups of Twisted Chevalley Groups over Commutative Rings |
| topic | Group Theory 20G35 |
| url | https://arxiv.org/abs/2502.04766 |