On discreteness of M\

Xi Fu

doi:10.4134/BKMS.2013.50.3.747

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Bull. Korean Math. Soc. 2013; 50(3): 747-752

Printed May 31, 2013

https://doi.org/10.4134/BKMS.2013.50.3.747

On discreteness of M\"{o}bius groups

Xi Fu

Shaoxing University

Abstract

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Abstract

It's known that one could use a fixed loxodromic or parabolic element in $M(\overline \br^n)$ as a test map to test the discreteness of a non-elementary M\"{o}bius group $G$. In this paper, we discuss the discreteness of $G$ by using a fixed elliptic element.

Keywords: discreteness, elliptic elements, loxodromic elements

MSC numbers: Primary 30F40; Secondary 20H10, 57S30