On Some Varieties of Soluble Lie Algebras

Abstract

In this paper, we study a class of soluble Lie algebras with variety relations that the commutator of $m$ and $n$ is zero. The aim of the paper is to consider the relationship between the Lie algebra $L$ with the variety relations and the Lie algebra $L$ which satisfies the permutation variety relations for the permutation $φ$ of $\{3, · · · , k\}$.