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For some exercise I required the fact that there are $p + 1$ lines in $\mathbb{F}_p \times \mathbb{F}_p$, where a line is defined as a $1$-dimensional subspace. This is easy to see, if we draw $\mathbb{F}_p \times \mathbb{F}_p$.

However, I also want to look at the lines in $\mathbb{P}^1(\mathbb{Z}/6\mathbb{Z})$. I have a hard time visualising this space. Is there an easy way to see this space and find out how many lines it has?

Krijn
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    "Lines" don't really work the same way since $\mathbb{Z}/6\mathbb{Z}$ isn't a field. What exactly do you mean by $\mathbb{P}^1(\mathbb{Z}/6\mathbb{Z})$? – Zev Chonoles Jun 20 '15 at 20:34
  • Well, that is actually part of the problem. I hoped that it was some sort of generalization of the finite planes of prime order to any natural number $n$, however I cannot seem to find a proper definition. My first thought was to look at lines in $\mathbb{Z}/6\mathbb{Z} \times \mathbb{Z}/6\mathbb{Z}$, however my instructor told me to look at $\mathbb{P}^1(\mathbb{Z}/6\mathbb{Z})$. – Krijn Jun 20 '15 at 20:52

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