The Study Related To Classical Groups Over Rings

In this paper, one type of maximal subgroups in symplectic groups over polynomial rings, one type of maximal subgroups in symplectic groups over local rings, are obtained. In this paper, We also determine all the overgroups of Sp(2m,R) in GL(2m,R) for R a local ring.In chapter 1, one type of maximal subgroups in symplectic groups overpolynomial rings are obtained. Let F be a field, R = F[X] be a ring of polynomial in one variable over F, m be a positive integer, f eF and S be the ideal of R generated by -f, We define:, then G(S) is a maximalsubgroups of Sp(2m,R).In chapter 2, one type of maximal subgroups in symplectic groups over local rings are obtained. Let R be a local ring and Char R≠ 2, mbea positive integer, S be the unique maximal ideal of R, We define.then G(S) is a maximal subgroups of Sp(2m,R).In chapter 3, We define all the overgroups of Sp{2m,R) in GL(2m,R) for R a local ring.