研究有限群的结构,以及有限群与其自同构之间的相互关系是有限群论中的重要课题。由于有限群的结构依赖于它的Sylow-子群在其中的嵌入方式。本项目正是从研究有限p-群的结构出发探讨满足下列条件的有限群G的结构以及它与其Sylow-子群的结构之间的关系。.1、G中任意非正规子群H，均有H的正规闭包包含(包含于)H的正规化子。.2、G中任意正规子群N，均有G'模(G'交N)循环或N模(N交Z(G))循环。.3、G中任意非正规交换子群均自中心化或者其正规化子等于中心化子。.进一步从有限群作用的角度来探讨其能平凡作用的最大正规子群。这样的研究将进一步推进Blackburn的定理。

Investigating the structure of finite groups, and the connection between the structure of finite groups and their automorphism groups are important topics in the theory of finite group. Because the structure of a finite group depends on its Sylow-subgroups embedded in it，this project is based on the study of finite p-groups structure to explore the structure of a finite group G that satisfies the following conditions and the connection between the structure of the finite group G and the structure of its Sylow-subgroups..1、For any non-normal subgroup H of G, the normal closures of H contains(is contained in) its normalizer..2、For any normal subgroup N of G, G' mod (G' meet N) is cyclic or N mod (N meet Z(G)) is cyclic..3、Any abelian non-normal subgroup of G is self-centered or its normalizer is equal to the centralizer..Furthermore, we use the technique of the action of groups on groups to discuss the maximal normal subgroup which can act trivially on another finite group. Such a study will further advance Blackburn's theorem.