The Influence Of Some Subgroups On The Structure Of Finite Groups

Since the Galois proposed the concept of permutable subgroup, the mathemati-cians also put forward the concepts for conjugate Permutable subgroup, permutablesubgroup and a series of subgroups definitions which based on this concept. Theystudied these subgroups on the impact of solvability. Wang Y.M. proposed the con-cept of c-normal subgroups and studied its impact on finite group. Some workersbased on these results defined weak c-normal subgroups, c-complemented subgroupand study their solvability and so on. In 2007, Yang G.C. propose a almost normalsubgroup which broader than c-normal subgroups, and study the structure of finitegroups with satisfied the properties of almost normal subgroup.Certain subgroups have a significant impact on the structure of the finitegroups. This paper studies the structure of the original group through the c-normalsubgroup almost normal subgroup, conjugate-permutable subgroup.The first chapter is an introduction, introduces the domestic and abroad re-search on the situation of the group theory, as well as the source and the maincontents of this paper.The second chapter, introduces the development content and research methodsof group theory.In the third chapter, studies the impact of the maximal subgroup Sylow sub-groups on the finite groups under the formal condition by using the definition andnature of the almost normal subgroups and given the su?cient condition of super-solvable of super-G.In the fourth chapter, studies c-normal subgroup nilpotency by using the natureof a new definition of V(G) in references [6].In the fifth chapter, the author weakens the conditions of subgroup of Frattini,any subgroup of G, into that any real subgroup Frattini is 1, so the nature ofnilpotent and supersolvable of group G.