A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-suppl...A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups.展开更多
Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = ...Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H N K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.展开更多
The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second comm...The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second commutator subgroup H''(γq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups .H(γq) are studied. Also, relations between them are given.展开更多
In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.
In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive se...In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive security) under three static(i.e. non q-based) assumptions. It is worth noting that only recently Waters gives a short ciphertext broadcast encryption system that is even adaptively secure under the simple assumptions. One feature of our methodology is that it is relatively simple to leverage our techniques to get adaptive security.展开更多
Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subg...Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable.展开更多
A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups...A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups. For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified, we report here some investigations on the computed Parabolic subgroups. This has been done with the utility of GAP.展开更多
Let F be a saturated formation of finite groups. Given a proper subgroup H of a group G, a subgroup H of G is called F-normal in G if G/HGbelongs to F; otherwise H is said to be F-abnormal in G. In this paper, we inve...Let F be a saturated formation of finite groups. Given a proper subgroup H of a group G, a subgroup H of G is called F-normal in G if G/HGbelongs to F; otherwise H is said to be F-abnormal in G. In this paper, we investigate the structure of a finite group by θ*-completions of F-abnormal subgroups.展开更多
All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting ...All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.展开更多
The medicinal moxa stick made by moxa wool combining with Chinese medicines of supporting the body resistance and strengthening the spleen was used to treat 74 cases of spleen deficiency, the other 41 patients as cont...The medicinal moxa stick made by moxa wool combining with Chinese medicines of supporting the body resistance and strengthening the spleen was used to treat 74 cases of spleen deficiency, the other 41 patients as control were treated by pure moxa stick. After treatment, the serum gastrin, urinary D - xylose excretory rate and T cell subgroups in patients with spleen deficiency have been greatly improved as compared with those before treatment in two groups (P< 0.01 or 0.05). Comparing the changes of the indexes between treatment group and control group, there were significant(P<0.05), or markedly significant(P<0.01) differences. It indicated that the medicinal moxibustion could improve the secreting and absorbing functions of digestive tract and the cellular immune function in patients with spleen deficiency.展开更多
A subgroup H of a group G is said to be primitive if it is a proper subgroup of the intersection of all subgroups of G containing H as its proper subgroup. The purpose of this note is to go further into the influence ...A subgroup H of a group G is said to be primitive if it is a proper subgroup of the intersection of all subgroups of G containing H as its proper subgroup. The purpose of this note is to go further into the influence of primitive subgroups on the structure of finite groups. Some new results are obtained.展开更多
Few studies have examined the effects of psy-chiatric disorders occurring over a long dura-tion among patients with chronic fatigue syn-drome (CFS). The role of premorbid and current psychiatric disorders in impairmen...Few studies have examined the effects of psy-chiatric disorders occurring over a long dura-tion among patients with chronic fatigue syn-drome (CFS). The role of premorbid and current psychiatric disorders in impairment was ex-plored with a sample of 113 participants with CFS. Subgroups were created based on past and current psychiatric status including those whose psychiatric history was premorbid and current, postmorbid and current, past but not current, and those with no lifetime diagnosis. Results from a one-way MANOVA revealed that patients with a premorbid and current psychiat-ric disorder reported significantly higher pain severity, more somatic symptoms, poorer sleep quality, and poorer quality of life than those with no psychiatric history. Levels of fatigue and physical functioning among patients with CFS were unrelated to the four subgroups in this study. Although those with a premorbid and current psychiatric disorder were differentiated from those with no psychiatric history on some markers of impairment, the sample as a whole had severe fatigue-related impairment, which is the cardinal symptom of CFS. Implications for research are discussed.展开更多
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
The present paper deals with a subgroup X of a group G is almost normal if the index |G: NG(X)| is finite, while X is nearly normal if it has finite index in the normal closure XG. This paper investigates the structur...The present paper deals with a subgroup X of a group G is almost normal if the index |G: NG(X)| is finite, while X is nearly normal if it has finite index in the normal closure XG. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.展开更多
In this paper,the authors introduce the discreteness criterion for n-dimensional subgroups in PU(1, n; C).These generalize the well-known discreteness criterion first established by T.Jorgensen.
The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case ...The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case of a cotorsion hull is important because endomorphisms in this class of groups are completely defined by their action on the torsion part and for mixed groups the ring of endomorphisms is isomorphic to the ring of endomorphisms of the torsion part if and only if the group is a fully invariant subgroup of the cotorsion hull of its torsion part. In the considered case, the cotorsion hull is not fully transitive and hence it is necessary to introduce a new function which differs from an indicator and assigns an infinite matrix to each element of the cotorsion hull. The relation ?difined on the set ?of these matrices is different from the relation proposed by the autor in the countable case and better discribes the lower semilattice. The use of the relation ?essentially simplifies the verification of the required properties. It is proved that the lattice of fully invariant subgroups of the group is isomorphic to the lattice of filters of the lower semilattice.展开更多
文摘A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups.
基金supported by the Deanship of Scientific Research(DSR) at King Abdulaziz University(KAU) represented by the Unit of Research Groups through the grant number(MG/31/01) for the group entitled "Abstract Algebra and its Applications"
文摘Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H N K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.
文摘The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second commutator subgroup H''(γq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups .H(γq) are studied. Also, relations between them are given.
基金Supported by SRFPYED(2017ZDX041)and SRFPYED(2016ZDX151)
文摘In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.
基金supported by the Nature Science Foundation of China under grant 60970119, 60803149the National Basic Research Program of China(973) under grant 2007CB311201
文摘In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive security) under three static(i.e. non q-based) assumptions. It is worth noting that only recently Waters gives a short ciphertext broadcast encryption system that is even adaptively secure under the simple assumptions. One feature of our methodology is that it is relatively simple to leverage our techniques to get adaptive security.
文摘Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable.
文摘A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups. For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified, we report here some investigations on the computed Parabolic subgroups. This has been done with the utility of GAP.
文摘Let F be a saturated formation of finite groups. Given a proper subgroup H of a group G, a subgroup H of G is called F-normal in G if G/HGbelongs to F; otherwise H is said to be F-abnormal in G. In this paper, we investigate the structure of a finite group by θ*-completions of F-abnormal subgroups.
基金The NSF (60776810,10871205) of Chinathe NSF (08JCYBJC13900) of Tianjin
文摘All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.
文摘The medicinal moxa stick made by moxa wool combining with Chinese medicines of supporting the body resistance and strengthening the spleen was used to treat 74 cases of spleen deficiency, the other 41 patients as control were treated by pure moxa stick. After treatment, the serum gastrin, urinary D - xylose excretory rate and T cell subgroups in patients with spleen deficiency have been greatly improved as compared with those before treatment in two groups (P< 0.01 or 0.05). Comparing the changes of the indexes between treatment group and control group, there were significant(P<0.05), or markedly significant(P<0.01) differences. It indicated that the medicinal moxibustion could improve the secreting and absorbing functions of digestive tract and the cellular immune function in patients with spleen deficiency.
文摘A subgroup H of a group G is said to be primitive if it is a proper subgroup of the intersection of all subgroups of G containing H as its proper subgroup. The purpose of this note is to go further into the influence of primitive subgroups on the structure of finite groups. Some new results are obtained.
文摘Few studies have examined the effects of psy-chiatric disorders occurring over a long dura-tion among patients with chronic fatigue syn-drome (CFS). The role of premorbid and current psychiatric disorders in impairment was ex-plored with a sample of 113 participants with CFS. Subgroups were created based on past and current psychiatric status including those whose psychiatric history was premorbid and current, postmorbid and current, past but not current, and those with no lifetime diagnosis. Results from a one-way MANOVA revealed that patients with a premorbid and current psychiat-ric disorder reported significantly higher pain severity, more somatic symptoms, poorer sleep quality, and poorer quality of life than those with no psychiatric history. Levels of fatigue and physical functioning among patients with CFS were unrelated to the four subgroups in this study. Although those with a premorbid and current psychiatric disorder were differentiated from those with no psychiatric history on some markers of impairment, the sample as a whole had severe fatigue-related impairment, which is the cardinal symptom of CFS. Implications for research are discussed.
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.
文摘The present paper deals with a subgroup X of a group G is almost normal if the index |G: NG(X)| is finite, while X is nearly normal if it has finite index in the normal closure XG. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.
基金Supported by the Scientific Research Foundation of Kaili University(Z1519)Guizhou Province Excellence Teacher Education Program(Mathematics and Applied Mathematics)
文摘In this paper,the authors introduce the discreteness criterion for n-dimensional subgroups in PU(1, n; C).These generalize the well-known discreteness criterion first established by T.Jorgensen.
文摘The paper considers the lattice of fully invariant subgroups of the cotorsion hull ?when a separable primary group T?is an arbitrary direct sum of torsion-complete groups.The investigation of this problem in the case of a cotorsion hull is important because endomorphisms in this class of groups are completely defined by their action on the torsion part and for mixed groups the ring of endomorphisms is isomorphic to the ring of endomorphisms of the torsion part if and only if the group is a fully invariant subgroup of the cotorsion hull of its torsion part. In the considered case, the cotorsion hull is not fully transitive and hence it is necessary to introduce a new function which differs from an indicator and assigns an infinite matrix to each element of the cotorsion hull. The relation ?difined on the set ?of these matrices is different from the relation proposed by the autor in the countable case and better discribes the lower semilattice. The use of the relation ?essentially simplifies the verification of the required properties. It is proved that the lattice of fully invariant subgroups of the group is isomorphic to the lattice of filters of the lower semilattice.
