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
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.
