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

Hamilton, Emily

doi:10.1090/proc/12904

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

Proc. Amer. Math. Soc. 144 (2016), 2327-2336

DOI: https://doi.org/10.1090/proc/12904

Published electronically: October 20, 2015

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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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