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This is not a Wikipedia article: It is an individual user's work-in-progress page, and may be incomplete and/or unreliable. For guidance on developing this draft, see Wikipedia:So you made a userspace draft. Find sources: Google (books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
Projective plane of order 3 | |
---|---|
Order | 3 |
Lenz-Barlotti Class | VII.2 |
Automorphisms | |
Point Orbit Lengths | 13 |
Line Orbit Lengths | 13 |
Properties | Desarguesian Self-dual |
Construction
editThis plane can be constructed using the standard vector space construction with a three-dimensional vector space over the finite field GF(3).
Ovals and Hyperovals
editThis plane has odd order, so by Qvist's theorem it does not have a hyperoval. Being a Desarguesian, this plane does have ovals, and by Segré's theorem, all ovals in this plane are conics, being the set of absolute points of an orthogonal polarity.
Subplanes
editSince this plane is a Desarguesian plane of prime order, it has no proper subplanes.
Unitals
editSince the order of this plane is not square, it does not have a unital.