A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map.In this paper,we give some new examples of Hom-groups,and show the first,second ...A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map.In this paper,we give some new examples of Hom-groups,and show the first,second and third isomorphism theorems of Hom-groups.We also introduce the notion of Hom-group action,and as an application,we prove the first Sylow theorem for Hom-groups along the line of group actions.展开更多
Structural mapping is an important method for studying algebraic structures.Hom-algebra and monoidal Hom-group are new structures produced by algebra and group structural mappings,respectively.These structures are imp...Structural mapping is an important method for studying algebraic structures.Hom-algebra and monoidal Hom-group are new structures produced by algebra and group structural mappings,respectively.These structures are important algebra and group generalizations and are closely related to them.Let(A,β)be a Hom-algebra and(G,α)a monoidal Hom-group.A structure of(A,β)graded by(G,α)is introduced;this structure is called Hom-group graded algebra.This study presents the definition of Hom group graded algebra,provides some examples,and dis-cusses its basic properties.Furthermore,a sufficient and necessary condition that makes(A,β)a strongly(G,α)-graded algebra is explored using a structure mapβand unit 1A.Finally,by using different maps,two sufficient and necessary conditions for a Hom-algebra to be a(G,α)-graded algebra are expressed in different ways.展开更多
基金Supported by NSF of Jilin Province(Grant No.YDZJ202201ZYTS589)NNSF of China(Grant Nos.12271085,12071405)the Fundamental Research Funds for the Central Universities。
文摘A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map.In this paper,we give some new examples of Hom-groups,and show the first,second and third isomorphism theorems of Hom-groups.We also introduce the notion of Hom-group action,and as an application,we prove the first Sylow theorem for Hom-groups along the line of group actions.
基金The National Natural Science Foundation of China (No. 12271089, 12471033)。
文摘Structural mapping is an important method for studying algebraic structures.Hom-algebra and monoidal Hom-group are new structures produced by algebra and group structural mappings,respectively.These structures are important algebra and group generalizations and are closely related to them.Let(A,β)be a Hom-algebra and(G,α)a monoidal Hom-group.A structure of(A,β)graded by(G,α)is introduced;this structure is called Hom-group graded algebra.This study presents the definition of Hom group graded algebra,provides some examples,and dis-cusses its basic properties.Furthermore,a sufficient and necessary condition that makes(A,β)a strongly(G,α)-graded algebra is explored using a structure mapβand unit 1A.Finally,by using different maps,two sufficient and necessary conditions for a Hom-algebra to be a(G,α)-graded algebra are expressed in different ways.
