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So I am suppose to show that the group of upper triangular matrices in $GL_n(\mathbb{R})$ say S, is Solvable but not nilpotent.

If we define $G_1 = S$, $G_2=[G_1, G_1]$, and $G_{i+1} = [G_i, G_i]$, Then to show that $S$ is solvable if at some point we have $G_N = \{id\}$. I am unable to find $G_2$. I got some information about it. I think it should be a subset of $SL_n(\mathbb{R})$ but I am unable to determine it precisely.

Also how should I determine $G_3$, $G_4 \dots \dots$ ?

GraduateStudent
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    https://math.stackexchange.com/questions/1753556/why-is-the-group-of-unit-upper-triangular-matrices-solvable – 1123581321 Sep 27 '20 at 13:10
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    https://math.stackexchange.com/questions/1965811/the-group-of-upper-triangular-matrices-in-gl-n-mathbbr-is-not-nilpotent?rq=1 – 1123581321 Sep 27 '20 at 13:20

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