About the simply-connectedness of algebraic groups

Question

Let $G$ be a simply-connected algebraic group. Is it necessarily true that its derived subgroup $G'$ is also simply-connected?

Answer 1

Yes, it is true. The definition of "simply-connected" refers to semisimple algebraic groups (and their classification) over an algebraically closed field: a semisimple algebraic group $G$ is simply-connected if every isogeny $G'\rightarrow G$ is an isomorphism. Since a semisimple group is equal to its derived subgroup, the claim is certainly true. A discussion about simply-connected algebraic groups with some references can be found here.