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
