局部环上正交群中一类子群的扩群

Overgroups of Certain Subgroups of Orthogonal Groups over Local Rings

定出了局部环上正交群中一类子群的扩群,得到了如下结果:设R是局部环,M是R的唯一极大理想,O(2m,R)为R上正交群.对R的任意理想S,G(2m,S)表示子群{A BC D∈O(2m,R)|B∈Sm×m}.如果char(R)≠2,m≥3,G(2m,0)≤X≤G(2m,M),那么存在R的理想S,使得X=G(2m,S).

A type of overgroups of certain subgroups of orthogonal groups are determined over local rings, with the result as follows： Let R be a local ring, M the unique maximal ideal of R, O（2m,R） an orthogonal group over R.G（2m,S） denotes the subgroup {（A B C D）∈O（2m,R）｜B∈S^m×m}for any ideal S of R. If char（R）≠2,m≥3,G（2m,0）≤X≤G（2m,M）,then there exists an ideal S of R such that X=G（2m,S）.