Derived metabelian groups from hv-groups

In this paper first we introduce and analyze a new definition of left and right commutators in Hv-group. Secondly, usingcommutators we introduce a new strongly equivalence relation π∗ on an Hv-group H such that the quotient H/π∗, the set of all equivalence classes, is a metabelian group. Then we introduce metabelian Hv-groups and investigate some of their properties. Finally, we investigate some properties of commutators for the class of weak polygroups.