局部环上辛群中一类子群的扩群格

Lattice of overgroups of certain subgroup of symplectic group over local rings

定出了局部环上辛群中一类子群的扩群格,得到了如下结果:设R是局部环,Sp(2m,R)为R上辛群,N表示子群{{AOC A′-1|}A∈GL(m,R),A′C=C′A}.如果2为R中的可逆元且m≥3,那么N在Sp(2m,R)的扩群格同构于R的理想格.作为推论得到了Sp(2m,R)的一类极大群.

The lattice of overgroups of certain subgroup of symplectic group was determined over local rings in this article,with the result as follows： Let R be a local ring,Sp（2m,R） a symplectic group over R,N the subgroup {{A O CA^′-1}｜A∈GL（m,R）,A′C=C′A}.If 2 was an invertible element in R and m≥3,then the lattice of overgroups of N in Sp（2m,R） was isomorphic to the lattice of ideals of R.As a corollary,a type of maximal subgroup of Sp（2m,R） was obtained.