局部环上伪辛群的生成

Generation of Pseudo-symplectic Group on Local Ring

目的对域F上典型群G(Fn,β)的生成问题、所得成果作了回顾,对局部环上伪辛群生成问题的研究作了一个展示.方法按展示的范式将G(Rn,β)映到G(Fn,β)上进行处理.结果在伪辛几何中,任一运动都可通过有限次平移来实现.结论给出了伪辛群的生成定理:伪辛群GPSn(R,β)存在有限生成系g={σ,λv|λ∈R,v∈Rn且β(v,v)=0}.

Objective To make the review on the obtained results of generation of the classical group G （F^n, β） over the field F, and to made a display on the study of the classical generation of the pseudosymplectic group over local rings. Method Dealing with this problem by mapping G （R^n, β） onto G （F^n, ^-β）. Resutlt In pseudo-symplectic geometry, any action can be achieved by finite trans lations. Conclusion The generation of pseudo-symplectic group theorem is given： The pseudo-symplectic group GPS. （R, β） exists finite generating system： g={σ,λv｜λ∈R,v∈Rn且β（v,v）=0}.