Volume 13, issue 1 (2013)

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Conservative subgroup separability for surfaces with boundary

Mark D Baker and Daryl Cooper

Algebraic & Geometric Topology 13 (2013) 115–125
Abstract

If $F$ is a compact surface with boundary, then a finitely generated subgroup without peripheral elements of $G={\pi }_{1}\left(F\right)$ can be separated from finitely many other elements of $G$ by a finite index subgroup of $G$ corresponding to a finite cover $\stackrel{̃}{F}$ with the same number of boundary components as $F$.

Keywords
subgroup separability
Mathematical Subject Classification 2010
Primary: 57M05
Secondary: 20E26, 57M07, 57M10, 57N05