A subgroup H of a group G is said to have the sub-cover-avoidance property in G ffthereis a chief series 1 = G0 ≤ G1 ≤…≤ Gn - G, such that Gi-1（H ∩ Gi） G for every i = 1,2,... ,l. In this paper, we give some...A subgroup H of a group G is said to have the sub-cover-avoidance property in G ffthereis a chief series 1 = G0 ≤ G1 ≤…≤ Gn - G, such that Gi-1（H ∩ Gi） G for every i = 1,2,... ,l. In this paper, we give some characteristic conditions for a group to be solvable under the assumptions that some subgroups of a group satisfy the sub-cover-avoidance property.展开更多
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
Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G. If d is the smallest generator number of P, then there exist maximal subgroups P1, P2,..., Pd of P, denoted by Md（P...Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G. If d is the smallest generator number of P, then there exist maximal subgroups P1, P2,..., Pd of P, denoted by Md（P） = {P1,...,Pd}, such that di=1 Pi = Φ（P）, the Frattini subgroup of P. In this paper, we will show that if each member of some fixed Md（P） is either p-cover-avoid or S-quasinormally embedded in G, then G is p-nilpotent. As applications, some further results are obtained.展开更多
In this paper, we study the cover-avoid property of -injectors on chief factors of a group G for a Fitting class in some universe with partial solubility.
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
群 G 的一个子群 H 称为在 G 中具有半覆盖远离性,如果存在 G 的一个主群列1=G_0＜ G_1＜…＜G_1=G,使得对每一 i=1,…,l 或者 H 覆盖 G_j/G_(j-1)或者 H 远离 G_j/G_(j-1)．本文证明了予群的半覆盖远离性是子群 C-正规性和子群的覆盖...群 G 的一个子群 H 称为在 G 中具有半覆盖远离性,如果存在 G 的一个主群列1=G_0＜ G_1＜…＜G_1=G,使得对每一 i=1,…,l 或者 H 覆盖 G_j/G_(j-1)或者 H 远离 G_j/G_(j-1)．本文证明了予群的半覆盖远离性是子群 C-正规性和子群的覆盖远离性之推广．进一步应用极大子群和 Sylow 子群给出了有限群为可解群的一些特征．展开更多
基金The NSF(10871210)of Chinathe NSF(06023728)of Guangdong Province
文摘A subgroup H of a group G is said to have the sub-cover-avoidance property in G ffthereis a chief series 1 = G0 ≤ G1 ≤…≤ Gn - G, such that Gi-1（H ∩ Gi） G for every i = 1,2,... ,l. In this paper, we give some characteristic conditions for a group to be solvable under the assumptions that some subgroups of a group satisfy the sub-cover-avoidance property.
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.10571181)the National Natural Science Foundation of Guangdong Province (Grant No.06023728) the Specialized Research Fund of Guangxi University (Grant No.DD051024)
文摘Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G. If d is the smallest generator number of P, then there exist maximal subgroups P1, P2,..., Pd of P, denoted by Md（P） = {P1,...,Pd}, such that di=1 Pi = Φ（P）, the Frattini subgroup of P. In this paper, we will show that if each member of some fixed Md（P） is either p-cover-avoid or S-quasinormally embedded in G, then G is p-nilpotent. As applications, some further results are obtained.
基金Research of the first author is supported by the Natural Science Foundation of Sandong Province （No. ZR2014AL001）, China.
文摘In this paper, we study the cover-avoid property of -injectors on chief factors of a group G for a Fitting class in some universe with partial solubility.
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.
文摘群 G 的一个子群 H 称为在 G 中具有半覆盖远离性,如果存在 G 的一个主群列1=G_0＜ G_1＜…＜G_1=G,使得对每一 i=1,…,l 或者 H 覆盖 G_j/G_(j-1)或者 H 远离 G_j/G_(j-1)．本文证明了予群的半覆盖远离性是子群 C-正规性和子群的覆盖远离性之推广．进一步应用极大子群和 Sylow 子群给出了有限群为可解群的一些特征．
