Strengthened Wiegold Conjecture in the Theory of Nilpotent Lie Algebras

In the present paper, we strengthen the assertion of the Wiegold conjecture for nilpotent Lie algebras over an infinite field by proving that if there exists a subset of a nilpotent Lie algebra $\mathfrak{g}$ consisting of elements of breadth not exceeding $n$ and satisfying some additional conditions, then the dimension of the commutator subalgebra $\mathfrak{g'}$ of $\mathfrak{g}$ does not exceed $n(n+1)/2$.