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Let Ma be the fractional maximal operators (0<a≤ 1 ) and (u, v ) a pair of weight functions, u ∈ D∞,σ=v^-1/(p-1)∈A∞,The boundedness of Ma on some homogenous groups (G,||·||, dx) and the covering Lemma of Calderon-Zygmund type are studied. Not only an