Number Theory pp 150-178 | Cite as

On cliques of exceptional units and Lenstra's construction of Euclidean fields

  • Armin Leutbecher
  • Gerhard Niklasch
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1380)


In the wake of a method for detecting Euclidean number fields with the aid of exceptional units, described in 1977 by H. W. Lenstra jr., we study a group action on cliques of exceptional units, determine the corresponding group and exploit the action in some concrete rings. This has also yielded 37 new Euclidean fields in degrees 5, 6, 7, 8, 9, and 10.

AMS subject classification

13F07 11R27 05C25 20B25 Euclidean number fields unit equation arithmetic graphs symmetric groups 


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Armin Leutbecher
    • 1
  • Gerhard Niklasch
    • 1
  1. 1.Mathematisches Institut der Technischen Universität MünchenMünchen 2Germany

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