 For an infinite group, the finite derived series may not stabilize, but the transfinite derived series always stabilizes.A group whose transfinite derived series reaches the trivial group is called a hypoabelian group, and every solvable group is a hypoabelian group.The first ordinal "α" such that "G"("α") = "G"("α"+1) is called the (transfinite) derived length of the group "G", and it has been shown that every ordinal is the derived length of some group .