一类特殊p-群自同构群的结构

The Structure of Auto-morphism Groups of Some Special p-groups

设G是p5阶有限群,对于群G具有一个循环极大子群,给出了它们所有互不同构的类型;利用半直积和全形的概念,得到了具有循环极大子群的p5阶群的自同构群的构造,同时也验证了具有这样性质的群是LA-群.所应用的方法可以用于解决所有具有循环极大子群的有限p-群及自同构群的构造.

Let G be a finite p-group,|G|=p5.The characteristic of the precise structure of the auto-morphism groups of groups of order p5,which have cyclic and maximal subgroups,is analyzed by the method of holomorph and semi-direct product.At the same time,It is proved that the groups with these properties are LA-groups.It has some practical significance to solve the famous LA-conjecture completely.The application of the method can be used to solve all finite p-groups,which have cyclic and maximal subgroups and autom...