Extension of Hölder’s theorem in

We prove that if Γ is a subgroup of Diff₊^\,1+ε(I) and N is a natural number such that every non-identity element of Γ has at most N fixed points, then Γ is solvable. If in addition Γ is a subgroup of Diff₊\,2(I) , then we can claim that Γ is meta-abelian.