On Hom-groups and Hom-group Actions  

作　　者：Liang Yun CHEN Tian Qi FENG Yao MA Ripan SAHA Hong Yi ZHANG 

机构地区：[1]School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,P.R.China [2]Department of Mathematics,Raiganj University,Raiganj 733134,West Bengal,India [3]School of Mathematical Sciences,Nankai University,Tianjin 300071,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第10期1887-1906,共20页数学学报（英文版）

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。

摘　　要：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.

关 键 词：Hom-groups Hom-subgroups Hom-quotient groups ISOMORPHISM Hom-group actions first Sylow theorem 

分 类 号：O152.5[理学—数学]