If everything is well define, does it exist a result like : (maybe some hypothesis are missing)
"Let $G$ be a simply connected algebraic group over a field $k$ and $N$ a normal algebraic subgroup of $G$ which is also simply connected. Then, $G/N$ is simply connected as quotient algebraic group." ?
Even if it's false, which book would you advise to learn stuff about simply connected, unipotent and solvable algebraic groups ?
Edit: Here G is connected, N is actually its derived group, and I say "simply connected" to say : "Does not have nontrivial etale group covering", where an etale group covering is an epimorphism of algebraic groups whose kernel (in the category of $k$-group scheme) is finite and etale