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, Γn),
the Clifford norm of
formula here
and the Clifford metric of SL(2, Γn) or of the Möbius group
M(ℝn)
formula here
where [mid ]·[mid ] is the norm of a Clifford number and
formula here
represents fi ∈ M(ℝn),
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.