Mathematica Bohemica, Vol. 147, No. 3, pp. 347-358, 2022
Endomorphism kernel property for finite groups
Heghine Ghumashyan, Jaroslav Guričan
Received October 28, 2020. Published online August 10, 2021.
Abstract: A group $G$ has the endomorphism kernel property (EKP) if every congruence relation $\theta$ on $G$ is the kernel of an endomorphism on $G$. In this note we show that all finite abelian groups have EKP and we show infinite series of finite non-abelian groups which have EKP.
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Affiliations: Heghine Ghumashyan, European University, 10 Davit Anhaght Street, Yerevan 0037, Armenia and Comenius University Bratislava, Šafárikovo námestie 6, 814 99 Bratislava, Slovakia, e-mail: hgumashyan@mail.ru; Jaroslav Guričan, Comenius University Bratislava, Šafárikovo námestie 6, 814 99 Bratislava, Slovakia, e-mail: gurican@fmph.uniba.sk
