A subgroup H of a finite group G is said to have the semi-cover-avoiding property in G if there is a chief series of G such that H covers or avoids every chief factor of the series. In this paper, some new results are...A subgroup H of a finite group G is said to have the semi-cover-avoiding property in G if there is a chief series of G such that H covers or avoids every chief factor of the series. In this paper, some new results are obtained based on the assumption that some subgroups have the semi-cover-avoiding property in the group.展开更多
In this paper, the so-called π-cover-avoiding properties of subgroups are defined and investigated. In terms of this property, we characterize the π-solvability of finite groups. Some other new results are also obta...In this paper, the so-called π-cover-avoiding properties of subgroups are defined and investigated. In terms of this property, we characterize the π-solvability of finite groups. Some other new results are also obtained based on the assumption that some subgroups have the semi cover-avoiding properties in a finite group.展开更多
基金the National Natural Science Foundation of China(10471085)the Shanghai Pujiang Program(05PJ14046)the Special Funds for Major Specialities of Shanghai Education Committee
文摘A subgroup H of a finite group G is said to have the semi-cover-avoiding property in G if there is a chief series of G such that H covers or avoids every chief factor of the series. In this paper, some new results are obtained based on the assumption that some subgroups have the semi-cover-avoiding property in the group.
基金Supported by the National Natural Science Foundation of China (Grant No. 10771132)the Science and Technology Foundation of Shanxi Province for Colleges (Grant No. 20081022)the Team Innovation Research Foundation of Shanxi University of Finance and Economics
文摘In this paper, the so-called π-cover-avoiding properties of subgroups are defined and investigated. In terms of this property, we characterize the π-solvability of finite groups. Some other new results are also obtained based on the assumption that some subgroups have the semi cover-avoiding properties in a finite group.
