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Annali di Matematica Pura ed Applicata

, Volume 54, Issue 1, pp 23–31 | Cite as

On a property of the moebius group

  • H. Schwerdtfeger
Article

Summary

It is shown that the group of all Moebius transformations (M. T.) contains a subgroup Open image in new window such that every non-involutory M. T. not in Open image in new window can be transformed into each of its conjugates outside the subgroup Open image in new window by a unique element of this subgroup. Hence every non-integral and non-involutory M. T. can be reduced into a normal form by means of a unique element of Open image in new window . Also a subgroup Open image in new window *, can be determined such that elements of Open image in new window * reduce all non-involutory M. T. not in Open image in new window *, into their classical (integral) normal forms. There is also a discussion of the question as to other fields over which the results remain valid.

References

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    F. Levi,Zur Irreduzibilität der Kreisteilungspolynome, «Compositio Mathematica», 1 (1933), 303–304.Google Scholar
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    H. Schwerdtfeger,Zur Geometrie der Moebius-Transformation, «Mathematische Nachrichten», 18 (1958), 168–172.zbMATHMathSciNetGoogle Scholar
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    H. Schwerdtfeger, «Geometry of the Complex Numbers, to appear in, «Mathematical Expositions», Toronto University Press 1961.Google Scholar
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    N. Tschebotaröw undH. Schwerdtfeger,Grundzüge der Galois'schen Theorie, «Noordhoff, Groningen 1950», p. 388.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1961

Authors and Affiliations

  • H. Schwerdtfeger
    • 1
  1. 1.MontrealCanada

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