On (2,3)-generation of matrix groups over the ring of integers, II
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M. A. Vsemirnov
Translated by: the author - St. Petersburg Math. J. 32 (2021), 865-884
- DOI: https://doi.org/10.1090/spmj/1674
- Published electronically: August 31, 2021
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Abstract:
Final steps are done in proving that the groups $\operatorname {SL}(n,\mathbb {Z})$, $\operatorname {GL}(n,\mathbb {Z})$ and $\operatorname {PGL}(n,\mathbb {Z})$ are $(2,3)$-generated if and only if $n\ge 5$, and $\operatorname {PSL}(n,\mathbb {Z})$ is $(2,3)$-generated if and only if $n=2$ or $n\ge 5$. In particular, the results cover the remaining cases of $n=8$, …, $12$, and $14$.References
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Bibliographic Information
- M. A. Vsemirnov
- Affiliation: St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia
- Email: vsemir@pdmi.ras.ru
- Received by editor(s): March 17, 2019
- Published electronically: August 31, 2021
- © Copyright 2021 American Mathematical Society
- Journal: St. Petersburg Math. J. 32 (2021), 865-884
- MSC (2020): Primary 20G30; Secondary 20F05
- DOI: https://doi.org/10.1090/spmj/1674
- MathSciNet review: 4167873