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On special congruence subgroups of symplectic groups
S. Tazhetdinov Kara-Kalpak State University
Abstract:
In this paper, it is proved that every special congruence subgroup $SSp(V,I)$ of the symplectic group $Sp(V(R))$, where $R$ is a ring of stable rank $1$ with invertible element $2$ and $\dim V(R)\ge 4$, is generated by the symplectic transvections belonging to this subgroup. This result is used to obtain the complete description of the normal subgroups of $Sp(V(R))$.
Received: 02.10.2000
Citation:
S. Tazhetdinov, “On special congruence subgroups of symplectic groups”, Mat. Zametki, 80:5 (2006), 770–772; Math. Notes, 80:5 (2006), 726–728
Linking options:
https://www.mathnet.ru/eng/mzm3086https://doi.org/10.4213/mzm3086 https://www.mathnet.ru/eng/mzm/v80/i5/p770
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