TY - JOUR

T1 - Subgroups of the general symplectic group containing the group of diagonal matrices

AU - Vavilov, N. A.

AU - Dybkova, E. V.

N1 - Copyright: Copyright 2007 Elsevier B.V., All rights reserved.

PY - 1984/2

Y1 - 1984/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0010894324&partnerID=8YFLogxK

U2 - 10.1007/BF01094368

DO - 10.1007/BF01094368

M3 - Article

AN - SCOPUS:0010894324

VL - 24

SP - 406

EP - 416

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -