The Burnside problem for $\text{Diff}_{\text{Vol}}(\mathbb{S}^2)$ Article Swipe

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Sebastián Hurtado , Alejandro Kocsard , Federico Rodríguez-Hertz ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1607.04603 · OA: W2492280057

Let $S$ be a closed surface and $\text{Diff}_{\text{Vol}}(S)$ be the group of volume preserving diffeomorphisms of $S$. A finitely generated group $G$ is periodic of bounded exponent if there exists $k \in \mathbb{N}$ such that every element of $G$ has order at most $k$. We show that every periodic group of bounded exponent $G \subset \text{Diff}_{\text{Vol}}(S)$ is a finite group.