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11th October 2017 3:30-4:30pm
room 745, Malet Street

Bruck nets and partial Sherk planes

In 1959, Bachmann characterised the finite Desarguesian affine planes of odd order as finite metric planes, which are point-line incidence geometries with a perpendicularity relation satisfying various axioms. In 1967, Sherk generalised the concept of a metric plane to characterise all finite affine planes of odd order. In this talk, we will discuss how to obtain an even larger class of geometries, the Bruck nets of even degree, by weakening Sherk's axioms to allow non-collinear pairs of points. This is joint work with John Bamberg and Jesse Lansdown.