Möbius Group
The Möbius transformations form a group under composition.
Theorem 5.4 (Möbius Group)
is a group.
Proof
Composition of functions is associative. The identity map is a Möbius transformation. If , then is its inverse, so every Möbius transformation has an inverse in the same set.
Related
Stated in
- Theorem 5.4 (Möbius Group)§5.2 The Möbius Group