Finite Abelian Groups with the Strong Endomorphism Kernel Property  

作　　者：Jie FANG Zhong Ju SUN 

机构地区：[1]School of Mathematics and Systems Science,Guangdong Polytechnic Normal University,Guangzhou 510665,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2020年第9期1076-1082,共7页数学学报（英文版）

基　　金：The authors would like to express their appreciation to the referee for helpful comments and suggestions.

摘　　要：An endomorphism h of a group G is said to be strong whenever for every congruenceθon G,(x,y)∈θimplies(h(x),h(y))∈θfor every x,y∈G.A group G is said to have the strong endomorphism kernel property if every congruence on G is the kernel of a strong endomorphism.In this note,we study the strong endomorphism kernel property in the class of Abelian groups.In particular,we show that a finite Abelian group has the strong endomorphism kernel property if and only if it is cyclic.

关 键 词：Strong ENDOMORPHISM KERNEL PROPERTY CONGRUENCE ABELIAN GROUP cyclic GROUP 

分 类 号：O152[理学—数学]