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Journal of Geometry

, Volume 18, Issue 1, pp 169–184 | Cite as

Zur Kennzeichnung von Lorentztransformationen in Endlichen Ebenen

  • Hans -Joachim Samaga
Article

Abstract

Given a commutative field K we define d(A,B):= (a1−b1)2−(a2−b2)2 for A=(a1,a2), B=(b1,b2) ε K2. Given moreover a fixed k ε KO, W. Benz has asked for all mappings σ: K2→K2 such that d(A,B)=k implies
. This paper gives an answer if K=GF(p), p=5,7,11: σ must be a bijective collineation in case p = 7,11; there are non-injective mappings in case p=5. To obtain some of these results we have mads use of a computer.

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Literatur

  1. [1]
    Benz, W.: On mappings preserving a single Lorentz — Minkowski — distance, I. Proc. Conf. (in memoriam Benjamino Segre) Rome 1981Google Scholar
  2. [2]
    Benz, W.: On mappings preserving a single Lorentz — Minkowskidistance, II. Erscheint im J. of GeometryGoogle Scholar
  3. [3]
    Benz, W.: On mappings preserving a single Lorentz — Minkowski — distance, III. Erscheint im J. of GeometryGoogle Scholar
  4. [4]
    Rado, F.: On the characterization of plane affine isometries. Resultate der Mathematik 3 (1980), 70–73.Google Scholar

Copyright information

© Birkhäuser Verlag 1982

Authors and Affiliations

  • Hans -Joachim Samaga
    • 1
  1. 1.Mathematisches SeminarUniversität HamburgHamburg 13

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