Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this pape...Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.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.
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, we investegate the intersection of a maximal intransitive subgroup with a maximal imprimitive subgroup. And, the structure of the second maximal intransitive subgroup of an alternating group is determined.
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 is called S-seminormal in a finite group G if H permutes with all Sylow p-subgroups of G with (p, |H| =1. The main object of this paper is to generalize some known results about finite supersolvable group...A subgroup H is called S-seminormal in a finite group G if H permutes with all Sylow p-subgroups of G with (p, |H| =1. The main object of this paper is to generalize some known results about finite supersolvable groups to a saturated formation containing the class of finite supersolvable groups.展开更多
In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems ab...In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.展开更多
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
Rapid diagnostic methods for classifying avian leukosis subgroups in the field were needed for routine, large-scale screening. As a first step in method development, we inserted the avian leukosis virus subgroup A (A...Rapid diagnostic methods for classifying avian leukosis subgroups in the field were needed for routine, large-scale screening. As a first step in method development, we inserted the avian leukosis virus subgroup A (ALV-A) env gene into plasmid pcDNA3.1/Zeo (+) and used this construct to transfect DF-1 cells. Zeocin-resistant cells were obtained after 2 weeks of zeocin selection. Then, the cells were analyzed using PCR, immunofluorescence, and Western blot for expression of the envA-encoded envelope protein after 30 serial passages. The DF-1/A cell line was completely resistant to 104 TCIDso/0.1 mL (50% tissue culture infective dose)ALV-A and was partially resistant to 10~ TCIDs0/0.1 mL ALV-A viral particles. By comparing the DF-1/A and DF-1 cell lines, an ALV-A isolate was identified using a gag-specific ELISAfor capsid protein p27. Thus, we established a DF-1/A cell line that was resistant to ALV-A infection. This cell line will be useful as a diagnostic tool.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
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
For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic de...For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.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
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
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
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.
基金Yibin University Pre-research Project,Research on the coupling and coordinated development ofmanufacturing and logistics industry under the background of intelligentmanufacturing,(2022YY001)Sichuan ProvincialDepartment of EducationWater Transport EconomicResearch Center,Research on the Development Path and Countermeasures of the Advanced Manufacturing Industry in the Sanjiang New District of Yibin under a“dual circulation”development pattern(SYJJ2020A06).
文摘Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.
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 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.
文摘In this paper, we investegate the intersection of a maximal intransitive subgroup with a maximal imprimitive subgroup. And, the structure of the second maximal intransitive subgroup of an alternating group is determined.
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A subgroup H is called S-seminormal in a finite group G if H permutes with all Sylow p-subgroups of G with (p, |H| =1. The main object of this paper is to generalize some known results about finite supersolvable groups to a saturated formation containing the class of finite supersolvable groups.
文摘In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.
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The work was founded by the National Key R&D Program of China(2016YFD0501606)the Public Industry Research Program,the Ministry of Agriculture of China(201203055)+2 种基金the Program of Science and Technology Development of Guangdong Province,China(2015A020209145)the China Meat-Type Chicken Research System(CARS-42-G09)the Modern Agriculture Talents Support Program,Ministry of Agriculture of China([2012] no.160)
文摘Rapid diagnostic methods for classifying avian leukosis subgroups in the field were needed for routine, large-scale screening. As a first step in method development, we inserted the avian leukosis virus subgroup A (ALV-A) env gene into plasmid pcDNA3.1/Zeo (+) and used this construct to transfect DF-1 cells. Zeocin-resistant cells were obtained after 2 weeks of zeocin selection. Then, the cells were analyzed using PCR, immunofluorescence, and Western blot for expression of the envA-encoded envelope protein after 30 serial passages. The DF-1/A cell line was completely resistant to 104 TCIDso/0.1 mL (50% tissue culture infective dose)ALV-A and was partially resistant to 10~ TCIDs0/0.1 mL ALV-A viral particles. By comparing the DF-1/A and DF-1 cell lines, an ALV-A isolate was identified using a gag-specific ELISAfor capsid protein p27. Thus, we established a DF-1/A cell line that was resistant to ALV-A infection. This cell line will be useful as a diagnostic tool.
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.
基金Supported by the NSF of China(11171194)by the NSF of Shanxi Province(2012011001-1)
文摘For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.
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.
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.
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.