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On rank 4 projective planes

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  • O. Bachmann

Abstract

Let a finite projective plane be called rank m plane if it admits a collineation group G of rank m , let it be called strong rank m plane if moreover G P = G 1 for some point-line pair ( P , 1 ) . It is well known that every rank 2 plane is desarguesian (Theorem of Ostrom and Wagner). It is conjectured that the only rank 3 plane is the plane of order 2. By [1] and [7] the only strong rank 3 plane is the plane of order 2. In this paper it is proved that no strong rank 4 plane exists.

Suggested Citation

  • O. Bachmann, 1981. "On rank 4 projective planes," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 4, pages 1-15, January.
    • Handle: RePEc:hin:jijmms:364361
    DOI: 10.1155/S0161171281000185
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