The Research On Some Questions Of Complete Configurations

This Article talks about a special complete configuration, and each line passes threepoints precisely.The realizasion of a configuration is one of the most important questions in this area. Inthechapter one, two meathods will be introduced. The first is used to construct a complicatedconfiguration by several simple ones, by the Descartes product. And the second one is toconstruct the configurations which cannot be constructed by the first meathod.In the chapter three and four, the features of configuration will be researched by means oftopology and algebra. It is proved that the configuration is not symmetric completely all the time byresearching their permutation group. And it will illustrate that two configurations even with the samequantities of points cannot be confirmed that they are identical by the thoary of isomorphism. At thesame time, the permutation group of Fano plane is researched deeply.The methods of realizing the configurations referred in the chapter one and two cannotbe used to construct all. So in the chapter five and six the hyper infinite configuration withn-dimension is shown, And all of the finite configurations with n dimension are the quotientspaces of the hyper infinite configuration. It is proved that a finite Transfiguration is decidedby its dimension and the configuration equations. So if exhausting all of the quotient spaces, all thefinite configurations will be discovered.