Residual finiteness of surface groups via tessellations (Q1317878)

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scientific article; zbMATH DE number 536875
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Residual finiteness of surface groups via tessellations
scientific article; zbMATH DE number 536875

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    Residual finiteness of surface groups via tessellations (English)
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    22 March 1994
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    \textit{P. Scott} [J. Lond. Math. Soc., II. Ser. 17, 555-565 (1978; Zbl 0412.57006)] has proved that the fundamental group \(G\) of a closed orientable surface is locally extended residually finite (LERF), which means that for any finitely generated subgroup \(S\) of \(G\) and any element \(g\) of \(G-S\) there exists a finite index subgroup \(H\) of \(G\) such that \(H\) contains \(S\) but not \(g\). For the proof, P. Scott used a tesselation of the hyperbolic plane by regular pentagons. Here the author presents an alternative proof using quadrangles instead of pentagons.
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    fundamental group
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    closed orientable surface
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    locally extended residually finite
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