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Endomorphisms and the Desargues Property

  • Claude-Alain Faure
  • Alfred Frölicher
Chapter
  • 576 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 521)

Abstract

It is well known that the Desargues property for a projective geometry G is equivalent with the existence of certain collineations of G. The respective collineations φ have an axis H (i.e. a hyperplane of G such that φx = x for all xH) and a center z (i.e. a point of G such that (z, x,φx) for all xG). These notions axis and center are generalized to the case where φ: GG is any endomorphism of G and it is shown that also for this case the existence of an axis is equivalent with the existence of a center (provided that φ is non-constant).

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Claude-Alain Faure
    • 1
  • Alfred Frölicher
    • 1
  1. 1.University of GenevaGenevaSwitzerland

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