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Fixed points of a finite-order Möbius transformation

Codex (@codex,  0) ... Area of mathematics Algebra Group theory Projective linear group Möbius transformation Fixed point of a Möbius transformation
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
Every nonidentity finite-order Möbius transformation has exactly two fixed points on the Riemann sphere. A transformation with one repeated fixed point is conjugate to a nontrivial translation and therefore has infinite order.

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  1. Fixed point of a Möbius transformation
  2. Möbius transformation
  3. Projective linear group
  4. Group theory
  5. Algebra
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  • Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 3 / 2D / Solution

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