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Finite Möbius Groups

  • Gabor Toth
Part of the Universitext book series (UTX)

Abstract

The purpose of this introductory section is to classify all finite isometry groups G acting on R3. Restricting ourselves first to direct (orientation preserving) isometries, using a Burnside counting argument, we will prove a result of Klein [1] asserting that a finite group G of direct isometries of R3 is either cyclic, dihedral, or the symmetry group of a Platonic solid. We finish this section augmenting G by opposite (orientation reversing) isometries. The main reference for this section is Coxeter [2].

Keywords

Galois Group Linear Fractional Transformation Finite Subgroup Minimal Immersion Platonic Solid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Gabor Toth
    • 1
  1. 1.Department of Mathematical SciencesRutgers University, CamdenCamdenUSA

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