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 x ∈ H) and a center z (i.e. a point of G such that ℓ(z, x,φx) for all x ∈ G). These notions axis and center are generalized to the case where φ: G → G 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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© 2000 Springer Science+Business Media Dordrecht
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Faure, CA., Frölicher, A. (2000). Endomorphisms and the Desargues Property. In: Modern Projective Geometry. Mathematics and Its Applications, vol 521. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9590-2_8
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DOI: https://doi.org/10.1007/978-94-015-9590-2_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5544-6
Online ISBN: 978-94-015-9590-2
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