SEMINAR: Groups and Combinatorics Seminar: Bruck nets and partial Sherk planes

Time and place: 16:00 Friday 29 April in Weatherburn LT

Speaker: Jesse Lansdown (UWA)

Title: Bruck nets and partial Sherk planes

Abstract: In Bachmann’s Aufbau der Geometrie aus dem Spiegelungsbegriff, it was shown that a finite metric plane is a Desarguesian affine plane of odd order equipped with a perpendicularity relation on lines, and conversely. Sherk 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 Bruck nets of even degree, by weakening Sherk’s axioms to allow non-collinear points.