© 2000 by London Mathematical Society
© The London Mathematical Society
On the Discreteness and Convergence in n-Dimensional Möbius Groups
Department of Mathematics, Shanghai Jiao Tong University Shanghai 200030, China
Received 19 January 1998. Revision received 15 February 1999.
Throughout this paper, we adopt the same notations as in [1, 6, 8] such as the Möbius group M(Rn), the Clifford algebra Cn–1, the Clifford matrix group SL(2, 
n), the Clifford norm of
 |
||A||=(|a|2+|b|2+|c|2+|d|2)
(1)
and the Clifford metric of SL(2, n) or of the Möbius group M(Rn)
d(A1,A2)=||A1–A2||(|a1–a2|2+|b1–b2|2+|c1–c2|2+|d1–d2|2) (2)
where |·| is the norm of a Clifford number and
 |
represents fi 
M(
), i = 1, 2, and so on. In addition, we adopt some notions in [6, 12]: the elementary group, the uniformly bounded torsion, and so on. For example, the definition of the uniformly bounded torsion is as follows.