I've been asked to give a proof that a finitely generated solvable group always has vanishing stable commutator length, as a part of an assignment for an infinite groups course.
I think the way to proceed is to use induction on derived length, taking the metabelian case as the base case for the induction.
I've only come across proofs using the fact that solvable groups are amenable groups, but these haven't been defined in this course.
Does anyone have any ideas?