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Extension of Hölder’s theorem in 
$\text{Diff}_{+}^{\,1+{\it\epsilon}}(I)$
Published online by Cambridge University Press: 11 February 2015
Abstract
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We prove that if 
${\rm\Gamma}$ is a subgroup of 
$\text{Diff}_{+}^{\,1+{\it\epsilon}}(I)$ and 
$N$ is a natural number such that every non-identity element of 
${\rm\Gamma}$ has at most 
$N$ fixed points, then 
${\rm\Gamma}$ is solvable. If in addition 
${\rm\Gamma}$ is a subgroup of 
$\text{Diff}_{+}^{\,2}(I)$ , then we can claim that 
${\rm\Gamma}$ is meta-abelian.
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