Annali di Matematica Pura ed Applicata

, Volume 88, Issue 1, pp 9–31 | Cite as

Linear representation of a class of projective planes in a four dimensional projective space

  • R. C. Bose
  • A. Barlotti


The theory of linear representations of projective planes developed by Bruck and one of the authors (Bose) in two earlier papers [J. Algebra1 (1964), pp. 85–102 and4 (1966), pp. 117–172] can be further extended by generalizing the concept of incidence adopted there. A linear representation is obtained for a class of non-Desarguesian projective planes illustrating this concept of generalized incidence. It is shown that in the finite case, the planes represented by the new construction are derived planes in the sense defined by Ostrom [Trans. Amer. Math Soc.111 (1964), pp. 1–18] and Albert [Boletin Soc. Mat. Mex,11 (1966), pp, 1–13] of the dual of translation planes which can be represented in a 4-space by the Bose-Bruck construction. An analogous interpretation is possible for the infinite case.


Projective Space Projective Plane Linear Representation Early Paper Translation Plane 
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Copyright information

© Nicola Zanichelli Editore 1971

Authors and Affiliations

  • R. C. Bose
    • 1
  • A. Barlotti
    • 2
  1. 1.USA
  2. 2.Italy

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