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Double coset separability of abelian subgroups of hyperbolic $ n$-orbifold groups


Author: Emily Hamilton
Journal: Proc. Amer. Math. Soc. 144 (2016), 2327-2336
MSC (2010): Primary 20E26, 57MO5
DOI: https://doi.org/10.1090/proc/12904
Published electronically: October 20, 2015
MathSciNet review: 3477050
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Abstract: A subset $ X$ of a group $ G$ is said to be separable if it is closed in the profinite topology. Let $ M = \mathbb{H}^n / \Gamma $ be a closed hyperbolic orbifold of dimension $ n \geq 2$. We show that if $ H$ and $ K$ are abelian subgroups of $ \Gamma $ and $ g \in \Gamma $, then the double coset $ HgK$ is separable in $ \Gamma $. We generalize this result to cocompact lattices in linear, semisimple Lie groups of (real) rank one.


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Additional Information

Emily Hamilton
Affiliation: Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407

DOI: https://doi.org/10.1090/proc/12904
Received by editor(s): October 26, 2014
Received by editor(s) in revised form: November 12, 2014, and July 2, 2015
Published electronically: October 20, 2015
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2015 American Mathematical Society