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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
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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- © Cambridge University Press, 2015