2
$\begingroup$

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.

  • 0
    Does 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_definition2012-07-01
  • 0
    @EricStucky No sorry, found that as well, but I could not make a link to the projectiv plane.2012-07-01
  • 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
  • 4
    Each 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
  • 0
    What 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

1 Answers 1