(?)-conditional Semipermutable Subgroups And Construction Of Finite Groups

In this paper,the thesis focuses on the (?)-conditional semipermutable of a finite group and aims at studying their influences on the structure of a finite group,such as p-supersolvability,supersolvability,and p-nilpotency,etc.At the same time,ss-quasinormality subgroup and c-normality subgroup are studied.We get some meaning results,and some known results are generalized.The article is mainly divided into two parts.The first part mainly proposes the concept of (?)-conditional semipermutable subgroups,that is,a Subgroup H of a group G is said to be (?)-conditional semipermutable if there exists an element x?G such that H permutes with conjugate of every member of 3 whose order is prime to |H|.And its influence structure of finite group(supersolvability and p-supersolvability).1.When the cyclic subgroups of normal subgroup are (?)-conditional semipermutable subgroup,the necessary and sufficient of the group to be p-supersolvable group are given and extended to the saturated system.2.The maximal subgroup of the Sylow subgroups of finite group are (?)-conditional semipermutable subgroup,some sufficient conditions the supersolvable group and the p-supersolvable group are given,and the relevent results are extended to the saturated system.The second part mainly studies the influence of ss-quasinormal subgroups and e normal subgroups on the structures of finite group.Using the "or" idea put forword by Professor Li Shirong,the ss-quasinormal subgroups and c-normal subgroups are combined to obtain a sufficient condition for the finite group p-nilpotent.50 references.