Normalizer of Twisted Chevalley Groups over Commutative Rings
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912285678632960 |
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| author | Garge, Shripad M. Makadiya, Deep H. |
| author_facet | Garge, Shripad M. Makadiya, Deep H. |
| contents | Let $R$ be a commutative ring with unity. Consider the twisted Chevalley group $G_{π, σ} (Φ, R)$ of type $ϕ$ over $R$ and its elementary subgroup $E'_{π, σ} (Φ, R)$. This paper investigates the normalizers of $E'_{π, σ}(Φ, R)$ and $G_{π, σ}(Φ, R)$ in the larger group $G_{π, σ}(Φ, S)$, where $S$ is an extension ring of $R$. We establish that under certain conditions on $R$ these normalizers coincide. Moreover, in the case of adjoint type groups, we show that they are precisely equal to $G_{π, σ}(Φ, R)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16894 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normalizer of Twisted Chevalley Groups over Commutative Rings Garge, Shripad M. Makadiya, Deep H. Group Theory 20G35 Let $R$ be a commutative ring with unity. Consider the twisted Chevalley group $G_{π, σ} (Φ, R)$ of type $ϕ$ over $R$ and its elementary subgroup $E'_{π, σ} (Φ, R)$. This paper investigates the normalizers of $E'_{π, σ}(Φ, R)$ and $G_{π, σ}(Φ, R)$ in the larger group $G_{π, σ}(Φ, S)$, where $S$ is an extension ring of $R$. We establish that under certain conditions on $R$ these normalizers coincide. Moreover, in the case of adjoint type groups, we show that they are precisely equal to $G_{π, σ}(Φ, R)$. |
| title | Normalizer of Twisted Chevalley Groups over Commutative Rings |
| topic | Group Theory 20G35 |
| url | https://arxiv.org/abs/2503.16894 |