Examining the Burnside Problem on Diff∞ ω (S2)
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Authors
Amatsuji-Berry, Max
Date
Type
thesis
Language
eng
Keyword
differential geometry , geometry , group theory , burnside problem , mathematics
Alternative Title
Abstract
Let $G$ be a group. $G$ is called \emph{periodic} if, for every element $g \in G$, there is a positive integer $n \in \N$ such that $g^n = \id_G$, and \emph{periodic of bounded exponent} if one such $n$ works for all $g \in G$. A question of interest in group theory asks whether $G$ being finitely generated and periodic (possibly periodic of bounded exponent) is enough to ensure that $G$ is finite. While this question is settled for arbitrary groups, it is still mostly open in the case where $G$ is a nonlinear transformation group acting on a manifold.
We follow the proof from Hurtado et al. that, in the case of $\Diff_{\omega}^{\infty} (\Sp^2)$, every finitely generated periodic subgroup of bounded exponent is finite, providing additional context that was passed over in its original presentation. We then discuss the results from the appendix of that paper, before concluding with some remarks on how one might approach this type of problem.
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This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-NonCommercial-NoDerivs 3.0 United States
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution-NonCommercial-NoDerivs 3.0 United States