Let $p \in \mathbb{N}$ be a prime number and $E$ the projective plane induced by the one and two dimensional linear subspaces of $(\mathbb{F}_p)^3$. I shall prove, that the characteristic of $E$ is equal to $p$. However I dont know what is meant by the characteristic of a projective plane and how it is defined. Can't find it anywhere.
What is the characteristic of a projective plane?
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linear-algebra
elementary-number-theory
projective-geometry
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0Does this mean anything to you? It's a topological definition of the Euler characteristic, so it should work for the projective plane, but it's pretty technical. http://en.wikipedia.org/wiki/Euler_characteristic#Topological_definition – 2012-07-01
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0@EricStucky No sorry, found that as well, but I could not make a link to the projectiv plane. – 2012-07-01
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0@anon, the projective plane in question is the finite geometry that has for its points the 1-dimensional subspaces of $(F_p)^3$ and for its lines the 2-dimensional subspaces. – 2012-07-02
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4Each time I see your [user name](http://www.dict.cc/german-english/hatschi.html) I feel the urge to say: **[Geeesundheit!!!](http://www.dict.cc/?s=gesundheit)**. This time I couldn't resist. – 2012-07-02
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0What was meant by the question was the **order** of the Projective plane, [described here](http://en.wikipedia.org/wiki/Projective_plane#Finite_field_planes). Don't ask me why they did call it characteristic on the homework sheet. Could be that it is the Euler characteristic of a projectiv plane, but I can't jugde on that one. – 2012-07-02