Uniform bounded elementary generation of Chevalley groups
| Autor: | Kunyavskii, Boris, Plotkin, Eugene, Vavilov, Nikolai |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\Phi$ of rank $\ge 2$ there exists a universal bound $L=L(\Phi)$ such that the simply connected Chevalley groups $G(\Phi,R)$ have elementary width $\le L$ for all Dedekind rings of arithmetic type $R$. Comment: 30 pages. arXiv admin note: text overlap with arXiv:2307.05526. Minor revision |
| Databáze: | arXiv |
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