Uniform bounded elementary generation of Chevalley groups
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866914673137287168 |
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| author | Kunyavskii, Boris Plotkin, Eugene Vavilov, Nikolai |
| author_facet | Kunyavskii, Boris Plotkin, Eugene Vavilov, Nikolai |
| contents | In this paper we establish a definitive result which almost completely closes the problem of bounded elementary generation for Chevalley groups of rank $\ge 2$ over arbitrary Dedekind rings $R$ of arithmetic type, with uniform bounds. Namely, we show that for every reduced irreducible root system $Φ$ of rank $\ge 2$ there exists a universal bound $L=L(Φ)$ such that the simply connected Chevalley groups $G(Φ,R)$ have elementary width $\le L$ for all Dedekind rings of arithmetic type $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15756 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform bounded elementary generation of Chevalley groups Kunyavskii, Boris Plotkin, Eugene Vavilov, Nikolai Group Theory 20G07 In this paper we establish a definitive result which almost completely closes the problem of bounded elementary generation for Chevalley groups of rank $\ge 2$ over arbitrary Dedekind rings $R$ of arithmetic type, with uniform bounds. Namely, we show that for every reduced irreducible root system $Φ$ of rank $\ge 2$ there exists a universal bound $L=L(Φ)$ such that the simply connected Chevalley groups $G(Φ,R)$ have elementary width $\le L$ for all Dedekind rings of arithmetic type $R$. |
| title | Uniform bounded elementary generation of Chevalley groups |
| topic | Group Theory 20G07 |
| url | https://arxiv.org/abs/2307.15756 |