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In this paper, we study the two weight commutators theorem of Riesz potential on an arbitrary homogeneous group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">H</mi></semantics></math></inline-formula> of dimension <i>N</i>. Moreover, in accordance with the results in the Euclidean space, we acquire the quantitative weighted bound on homogeneous group.