Korean J. Math. Vol. 30 No. 3 (2022) pp.513-524
DOI: https://doi.org/10.11568/kjm.2022.30.3.513

Epis, dominions and zigzag theorem in commutative groups

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Published: Sep 30, 2022
Keywords:
Tensor product, Commutative Groups, Epimorphisms, Dominions, Zigzag
Mathematics Subject Classification:
06F05, 20M07, 20M10

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Aftab Hussain Shah
Department of Mathematics, Central University of Kashmir, Ganderbal 191131, India
Muneer Nabi
Department of Mathematics, Central University of Kashmir, Ganderbal 191131, India
Shabir Ahmad Ahanger
Department of Mathematics, Central University of Kashmir, Ganderbal 191131, India

Abstract

In this paper, we introduce the notion of tensor product in groups and prove its existence and uniqueness. Next, we provide the Isbell's zigzag theorem for dominions in commutative groups. We then show that in the category of commutative groups dominions are trivial. This enables us to deduce a well known result epis are surjective in the category of commutative groups.


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