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.
Keywords:  endomorphism kernel property; nilpotent group; $p$-group
Classification MSC:  08A35, 20D15, 20K01, 20K27, 20K30


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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


 
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