Is every solvable abelian?

Could you please clarify your question? Are you asking if every solvable group is necessarily abelian? If so, the answer is no. A solvable group is a group that has a composition series, meaning it can be broken down into a sequence of subgroups such that each is normal in the next and the sequence ends in the trivial group. However, this does not necessarily mean that the group itself is abelian, as there are solvable groups that are not abelian. For example, the symmetric group S3 on three elements is solvable but not abelian.