| It is well known that subgroups of finite groups play an important role ininvestigating the structure and properties of finite groups. For instance, ourusual methods to investigate the structure and properties of a group are usingmaximal subgroups,2-maximal subgroups even n-maximal subgroups. Hencestudying finite groups by subgroups with certain properties is widely concerned.In this thesis, we investigate the structure of finite groups under the assumptionof partial subgroups. Not only many known results are generalized, but also thestudy of maximal subgroups is perfected.In Chapter3we investigate the structure of finite groups by a class of non-nilpotent proper subgroups under some assumption, which is called a Schmidtcovering. Our results enrich some important theorems on maximal subgroups and2-maximal subgroups, and also generalize the known results of O. J. Schmidt onminimal non-nilpotent groups. In Chapter4, based on the conception of Schmidtcovering of a finite group, we define generalized Schmidt covering of finite groups.It is a proper generalization of the class of groups whose maximal subgroups areeither nilpotent or normal, which was investigated by J. S. Rose. In Chapter5we introduce the concept of non-supersolvable covering, which is composed bycertain proper non-supersolvable subgroups with certain conditions. Our resultgeneralize the known results of B. Huppert on minimal non-supersolvable groups.In Chapter6we give the definition of H S-subgroups of finite groups. It is ageneralization of H C-subgroups, which is proposed by Doctor X. B. Wei andProfessor X. Y. Guo. Also, we get some necessary and sufcient conditions onp-nilpotence and supersolvability of finite groups. |
