It is known that the dimension of Schur multiplier a non-abelian nilpotent Lie algebra L n equal to 1 2 (n − 1)(n 2) + s(L) for some ≥ 0. The structure all algebras has been given ≤ 4 in several

For a $p$-group of order $p^n$, it is known that the $2$-nilpotent multiplier equal to $|\mathcal{M}^{(2)}(G)|=p^{\f12n(n-1)(n-2)+3-s_2(G)}$ for an integer $s_2(G)$. In this article, we characterize all non abelian $p$-groups satisfying in $s_2(G)\in\{1,2,3\}.

Let L be an n-dimensional non-abelian nilpotent Lie algebra and $$ s(L)=\frac{1}{2}(n-1)(n-2)+1-\dim {\mathcal {M}}(L) where is the Schur multiplier of a L. The structures algebras when s(L)\in \lbrace 0,1,2,3,4,5\rbrace are determined. In this paper, we classify all s(L)=6,7.