Let be positive integers and be non-zero integers. We denote by the class of groups in which, for every subset of of cardinality , there exist a subset , with ,, and a function , with such that where , . The class is defined exactly as , with additional conditions " whenever , where ". Let G be a finitely generated residually finite group. Here we prove that (1) If , then has a normal nilpotent subgroup with finite index such that the nilpotency class of is bounded by a function of , where , is the torsion subgroup of . (2) If be generated, then has a normal nilpotent subgroup whose index and the nilpotency class are bounded by a function of .