摘要
设R是局部环 ,I1,I2 是R中任意固定的且为不同时等于R的理想 ,S I1,T I2 为R的任意两个理想 ,GL(n ,R)是R上n级一般线性群 ,G(n ,r ,S ,T)表示子群A BC D ∈GL(n ,R)B∈Sr×(n-r) ,C∈T(n-r)×r .当n≥ 4 ,1 ≤r<n ,max(r,n-r) ≥ 3时 ,定出了G(n ,r,0 ,0 )在G(n ,r,I1,I2 )中的全部扩群 .
Let R be a local ring, I 1, I 2 two fixed ideals both of which are not R, SI 1 and TI 2 two ideals of R, GL(n,R) the General Linear Group over R. G(n,r,S,T) denotes the subgroup A BC D∈GL(n,R)B∈S r×(n-r) ,C∈T (n-r)×r . In this paper, all the overgroups of G(n,r,0,0) in G(n,r,I 1,I 2) are determined, for n≥4,1≤r<n,\%max\%(r,n-r)≥3.
关键词
局部环
线性群
扩群
local ring
linear group
overgroups
