PSU(3,q^2)和线性空间自同构群

PSU(3,q^2)and the automorphism groups of linear spaces.

用置换群和抽象群的理论研究PSU(3,q2)的某些子群结构,并应用到射影平面上.得到主要结果:令q是素数方幂,若G是一个射影平面的共线变换群并且传递地作用在点集合上,则G不能与PSU(3,q2)同构.

Based on the theory of permutation groups and abstract groups, some subgroups of PSU(3,q^2) are investigated. These results are then applied to the research on projective planes. The main result: Let q be a power of a prime, and if G is a collineation group of a projective plane and G acts transitively on the points, then G is not isomorphic to PSU(3,q^2).