This is my first question, so my apologies if it is too simple/poorly motivated.
During the course of some recent research I came across a particular variant of the following problem.
Let $G$ contain a normal unipotent subgroup $N$, where $R$ is a unital commutative ring of characteristic zero, $n\geq 4$, and it is assumed that $G/N$ is unipotent. Is it true that $G$ is also unipotent? What if $N$ is isomorphic to a subgroup of $U(n,R)$; the group of upper uni-triangular matrices?
It is somewhat well known, and I believe has already been answered on this site, that for $G$ an algebraic group and $N$ a normal closed subgroup, then the answer is in the affirmative.
Unfortunately, all of the literature I have read over the last few weeks points to results of this kind always being proven when replacing $R$ by an algebraically closed field or by a finite field, or only considering the case $n=3$.
Even if the original question cannot be answered entirely, any non-trivial examples of such $R$ would be enlightening. Otherwise, I would be satisfied to know if there are any similarly general results if $G$ is not taken to be an algebraic group and/or $R$ is a ring of characteristic zero.
Thank you for the helpful comments. Unfortunately, I am no expert with regards to algebraic geometry.