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

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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