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There are described the subgroups of the general symplectic group Γ=GSp(2n, R) over a commutative semilocal ring R, containing the group of symplectic diagonal matrices. For each such subgroup P there is uniquely defined a symplectic D-net a such that Γ(σ)≤p≤NΓ(σ), where Γ (σ) is the net subgroup in Γ corresponding to σ (cf. RZhMat, 1977, 5A288), and NΓ(σ) is its normalizer. The quotient group NΓ × (σ)/Γ(σ) is calculated. There are also considered subgroups in Sp(2n, R). Analogous results for subgroups of the general linear group were obtained earlier in RZhMat, 1978, 9A237.
Original language | English |
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Pages (from-to) | 406-416 |
Number of pages | 11 |
Journal | Journal of Soviet Mathematics |
Volume | 24 |
Issue number | 4 |
DOIs | |
State | Published - Feb 1984 |
ID: 76483735