Abstract
An endomorphism h of a group G is said to be strong whenever for every congruence θ on G, (x,y) ∈ θ implies (h(x), h(y)) ∈ θ for 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.
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Fang, J., Sun, Z.J. Finite Abelian Groups with the Strong Endomorphism Kernel Property. Acta. Math. Sin.-English Ser. 36, 1076–1082 (2020). https://doi.org/10.1007/s10114-020-9444-8
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DOI: https://doi.org/10.1007/s10114-020-9444-8