A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditional...A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditionally permutability of some 2-maximal subgroups of the Sylow subgroup of G, on the structure of finite groups. New criteria for a group G being p-nilpotent are obtained.展开更多
A subgroup H of a group G is called s-conditionally permutable in G if for every Sylow subgroup T of G there exists an element x ∈ G such that HTx = TxH. Using the concept of s-conditionally permutable subgroups, som...A subgroup H of a group G is called s-conditionally permutable in G if for every Sylow subgroup T of G there exists an element x ∈ G such that HTx = TxH. Using the concept of s-conditionally permutable subgroups, some new characterizations of finite groups are obtained and several interesting results are generalized.展开更多
A subgroup H of a finite group G is said to be permutable in G if it permutes with every subgroup of G. In this paper, we determine the finite groups which have a permutable subgroup of prime order and whose maximal s...A subgroup H of a finite group G is said to be permutable in G if it permutes with every subgroup of G. In this paper, we determine the finite groups which have a permutable subgroup of prime order and whose maximal subgroups are totally （generalized） smooth groups.展开更多
We introduce the 2D dimensional double space with the coordinates Z^M=（x~μ,y_μ）,whose components are the coordinates of initial space x~μ and its T-dual y_μ.We shall show that in this extended space the T-dualit...We introduce the 2D dimensional double space with the coordinates Z^M=（x~μ,y_μ）,whose components are the coordinates of initial space x~μ and its T-dual y_μ.We shall show that in this extended space the T-duality transformations can be realized simply by exchanging the places of some coordinates x^a,along which we want to perform T-duality,and the corresponding dual coordinates y_a.In such an approach it is evident that T-duality leads to the physically equivalent theory and that a complete set of T-duality transformations forms a subgroup of the 2D permutation group.So,in double space we are able to represent the backgrounds of all T-dual theories in a unified manner.展开更多
基金The Scientific Research Foundation of Sichuan Provincial Education Department of China(No.08zb082)
文摘A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditionally permutability of some 2-maximal subgroups of the Sylow subgroup of G, on the structure of finite groups. New criteria for a group G being p-nilpotent are obtained.
基金supported by National Natural Science Foundation of China (Grant No. 10771180)Scientific Research Fund of Sichuan Provincial Education Department (Grant No. 08zb059)Research Programme of Chengdu University of Information Technology
文摘A subgroup H of a group G is called s-conditionally permutable in G if for every Sylow subgroup T of G there exists an element x ∈ G such that HTx = TxH. Using the concept of s-conditionally permutable subgroups, some new characterizations of finite groups are obtained and several interesting results are generalized.
文摘A subgroup H of a finite group G is said to be permutable in G if it permutes with every subgroup of G. In this paper, we determine the finite groups which have a permutable subgroup of prime order and whose maximal subgroups are totally （generalized） smooth groups.
基金Supported by the Serbian Ministry of Education and Science(171031)
文摘We introduce the 2D dimensional double space with the coordinates Z^M=（x~μ,y_μ）,whose components are the coordinates of initial space x~μ and its T-dual y_μ.We shall show that in this extended space the T-duality transformations can be realized simply by exchanging the places of some coordinates x^a,along which we want to perform T-duality,and the corresponding dual coordinates y_a.In such an approach it is evident that T-duality leads to the physically equivalent theory and that a complete set of T-duality transformations forms a subgroup of the 2D permutation group.So,in double space we are able to represent the backgrounds of all T-dual theories in a unified manner.
