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 $Sp(V(R))$.

UDC: 514.154+519.45

Received: 02.10.2000

DOI: 10.4213/mzm3086

 English version: Mathematical Notes, 2006, 80:5, 726–728

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