Elliptic elements in Möbius groups. (Q731370)

The discreteness of Möbius groups is a fundamental problem which has been discussed by many authors. In 1976, \textit{T. Jørgensen} established a discreteness criterion by using the well-known Jørgensen inequality [Am. J. Math. 98, 739-749 (1976; Zbl 0336.30007)]. This criterion has become standard in the literature. Afterwards many authors tried to generalize it. In this paper, the author, under a restriction on \(\dim(M_G)\), gives the discreteness criterion by the following theorem. Theorem: Let \(G\subset\text{Isom}(H^n)\) be a nonelementary subgroup and \(\dim(M_G)\) be even. If \(G\) contains an elliptic element, then \(G\) is discrete if and only if \(WY(G)\) is discrete and each nonelementary subgroup of \(G\) generated by two elliptic elements is discrete.