Do Mobius Maps Form a Simple Group?

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SUMMARY

The set of all Möbius maps forms a simple group, meaning it has no non-trivial subgroups. To prove this, one must demonstrate that any subgroup of Möbius transformations is either trivial or the entire group. Characterizing non-trivial subgroups involves understanding the properties of Möbius transformations and their action on the Riemann sphere.

PREREQUISITES
  • Understanding of Möbius transformations
  • Familiarity with group theory concepts
  • Knowledge of the Riemann sphere
  • Basic skills in abstract algebra
NEXT STEPS
  • Study the properties of Möbius transformations in detail
  • Learn about simple groups in group theory
  • Explore the action of groups on the Riemann sphere
  • Investigate the classification of subgroups in abstract algebra
USEFUL FOR

Mathematicians, students of abstract algebra, and anyone interested in group theory and its applications in complex analysis.

AlbertEinstein
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Hi all,

How do I prove that the set of all Mobius Maps form a simple group, that is they have no non-trivial subgroup? How can I characterize a non-trivial subgroup? Hints will be welcome.

Thanks
 
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hi guys, please help.
 

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