群论在网络理论中的应用研究

Study on the Application of Group Theory in Network Theory

本用群论研究了双口网络集合，双口理想变换器与器件的集合，２ｎ端口理想变换器和器件的集合。研究的结果表明，双口网络集合的级联构成乘法群，双口网络集合的串、并联构成加法群，双口理想变换器和器件的集合之间存在子群与陪集的关系。２ｎ端口变换器和器件集合之间同样存在子群与陪集的关系。应用群论使网络理论中彼此孤立的变换器相互联系，并可以由一类变换器产生另一类变换器。

Group theory is applied to study two-port network set,two-port ideal coverter and devices set,2n-port ideal converter and devices set.It is shown that cascade connection type two-port networks set make multiplication group,and parellel or series connection type two-port networks make addition group.Between two-port real converter and devices set ,as well as 2n-port lead converter and devices set,exist the relation between subgroup and coset.It applys.It is shown that the application of group theory makes separate converters in netwrk theory interrelated to each othor ,and produces a method to convert a converter from one kind to another.