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
In this paper .an important property layer-preserving of LF group and an concept LF λ-subgroup generated by LF subset will be introduced. On the height of LF group theory ,we recognize the concept generated subgroup ...In this paper .an important property layer-preserving of LF group and an concept LF λ-subgroup generated by LF subset will be introduced. On the height of LF group theory ,we recognize the concept generated subgroup more clearly.展开更多
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
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
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
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In this paper .an important property layer-preserving of LF group and an concept LF λ-subgroup generated by LF subset will be introduced. On the height of LF group theory ,we recognize the concept generated subgroup more clearly.
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 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.
