Suppose $A$ is a Lie algebra on field $F_{p}$ with $[A,A,A]=0$. Denote $\{a_{1},\cdots,a_{d}\}$ is a minimal generating set of $A$.It's possible that $[a_{i},a_{j}]=0$ for some $1\leq i<j\leq d$ and $[a_{s_{1}},a_{t_{1}}]=[a_{s_{2}},a_{t_{2}}]$ where $1\leq s_{k}<t_{k}\leq d$ and $\{s_{1},t_{1}\}\neq\{s_{2},t_{2}\}$. My question is that if $\{[a_{i},a_{j}]|[a_{i},a_{j}]\neq0\}$ are Linearly independent by select appropriate minimal generating set
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