How does one show that Derived Algebra is nilpotent implies the lie algebra is solvable.
My attempt: Let $L$ be such a Lie-algebra then $[L,L]$ is nilpotent so it is solvable. So $[L,L]^{(n)}=0$ for some $n$. What can I do after this?
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$[L, L] = L^{(2)}$. – Andreas Caranti Feb 09 '16 at 12:05
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2Hint: Both $[L,L]$ and $L/[L,L]$ are solvable, so...? – Tobias Kildetoft Feb 09 '16 at 12:05
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@DietrichBurde That seems mainly focused on the (much harder) converse of this problem. – Tobias Kildetoft Feb 09 '16 at 13:32