• DOI:10.1017/S144678871700009X
• Corpus ID: 119636019

BRUCK NETS AND PARTIAL SHERK PLANES

@article{Bamberg2016BRUCKNA,
  title={BRUCK NETS AND PARTIAL SHERK PLANES},
  author={John Bamberg and Joanna B. Fawcett and Jesse Lansdown},
  journal={Journal of the Australian Mathematical Society},
  year={2016},
  volume={104},
  pages={1 - 12}
}

• J. Bamberg, Joanna B. Fawcett, Jesse Lansdown
• Published 27 January 2016
• Mathematics
• Journal of the Australian Mathematical Society

In Bachmann [Aufbau der Geometrie aus dem Spiegelungsbegriff, Die Grundlehren der mathematischen Wissenschaften, Bd. XCVI (Springer, Berlin–Göttingen–Heidelberg, 1959)], it was shown that a finite metric plane is a Desarguesian affine plane of odd order equipped with a perpendicularity relation on lines and that the converse is also true. Sherk [‘Finite incidence structures with orthogonality’, Canad. J. Math. 19 (1967), 1078–1083] generalised this result to characterise the finite affine planes of odd order by removing the ‘three reflections axioms’ from a metric plane. We show that one can obtain a larger class of natural finite geometries, the so-called Bruck nets of even degree, by weakening Sherk’s axioms to allow noncollinear points.