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Let L be an n-dimensional nilpotent Lie algebra of nilpotency class c with the derived subalgebra of dimension m. Recently, Rai proved that the dimension of Schur multiplier of L is bounded by 
. In this paper, in virtue of a recent bound of Rai, we give the structure of all nilpotent Lie algebras that attain this bound.
Mathematics Subject Classification (2010):
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