# symplectic group meaning in Chinese

## Examples

1. 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
本文主要研究了多项式环上辛群的一类子群的极大性，局部环上辛群的一类子群的极大性和局部环上辛群在线性群中的扩群
2. 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 )
在第二章中，得到了局部环上辛群的一类极大子群：设r是一个特征不为2的局部环， m是个正整数， s是r的唯一极大理想，则g ( s )是sp ( 2m ， r )的一个极大子群。
3. This paper is to study harmonic maps into symplectic groups and local isometric immersions into space forms by means of the soliton theory . by realizing an action of the rational loop group on the spaces of corrsponding solutions , we get the backlund transformation and the darboux transformation , and thereby we give the explicit construction for harmonic maps into symplectic groups and local isometric immersions into space forms via purely algebraic algorithm
主要用孤立子理论研究到辛群的调和映射和到空间形式的局部等距浸入，通过有理loop群在其解空间上的dressing作用，给出b icklund变换和darboux变换的显式表示，从而获得到辛群及其对称空间的调和映射和到空间形式的局部等距浸入的纯代数构造方法。
4. In chapter 1 , one type of maximal subgroups in symplectic groups over polynomial 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 maximal subgroups of sp ( 2m , r )
在第一章中，得到了多项式环上辛群的一类极大子群：设f是一个域， r = f [ ]是域f上关于的一元多项式环， m是一个正整数， f f ， s是r的由- f生成的理想，则是sp ( 2m ， r )的一个极大子群。
5. Its content may be separated into two parts . the first part contains chapter one and chapter two , which treat of the harmonic maps from surface into symplectic groups and quaternion grassmann manifolds . the second part contains chapter three and chapter four , which treat of local isometric immersions from space forms or riemannian products of space forms into space forms
全文分四章，内容可分为两部分：第一部分包括第一、二章，主要论涉从曲面到辛群及四元grassmann流形的调和映射；第二部分包括第三、四章，主要论涉从空间形式或空间形式的局部riemann积到空间形式的局部等距浸入。

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