In this paper, the notion of H-sets on Hv-groups is introduced and some related properties are investigated and some examples are given. In this regards, the concept of regular, strongly regular relations and homomorphism of H-sets are adopted. Also, the classical isomorphism theorems of groups are generalized to H-sets on Hv-groups. Finally, by using these concepts tensor product on Hv-groups is introduced and
proved that the tensor product exists and is unique up to isomorphism.
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