Hughes plane
In mathematics, a Hughes plane is one of the non-Desarguesian projective planes found by Daniel Hughes (1957). There are examples of order p2n for every odd prime p and every positive integer n.
The construction of a Hughes plane is based on a nearfield N of order p2n for p an odd prime whose kernel K has order pn and coincides with the center of N.
A Hughes plane H:
The Hughes plane of order 9 was actually found earlier by Veblen and Wedderburn in 1907. A construction of this plane can be found in Room & Kirkpatrick (1971) where it is called the plane Ψ.
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