Title is the entire question: Are projective planes of order n unique up to an isomorphism?
If so is there a simple proof for this?
2026-03-30 00:21:06.1774830066
Are projective planes of order n unique up to an isomorphism?
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No. There are non-Desarguesian planes of order $p^2$ with $p$ an odd prime, for instance the Hall plane.
The classical projective planes defined by finite fields are Desarguesian.