Complex Lie algebra $\mathfrak{g}$ is solvable implies that $\mathfrak{g}'$ is nilpotent.
67842
Solvable equivalent to nilpotency of first derived Lie algebra?
133758
Traces of powers of a matrix $A$ over an algebra are zero implies $A$ nilpotent.
34724
For $G$ a group and $H\unlhd G$, then $G$ is solvable iff $H$ and $G/H$ are solvable?
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
116159
Derivations on semisimple Lie algebra
30794
Commutator Group of $GL_2(R)$ is $SL_2(R)$
50236
Solvable Lie algebra with codimension 1 ideal
62219
Under what conditions is the exponential map on a Lie algebra injective?
133046
Showing $[L,rad(L)]$ is nilpotent.
114569
How do you find the Lie algebra of a Lie group (in practice)?
88726
Problem about solvable groups
77722
Lie algebra of affine linear maps
25009
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent
105666
What's an easy way to show that $GL(n,\mathbb C)$ is connected?
128603
Lie algebra and tangent space at the identity are isomorphic
125980
Isomorphic Lie Algebra $so(4)$ and $su(2) \times su(2)$
92837
Solvable and nilpotent groups, normal series and intuition