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Fano plane

Contents

Idea

The Fano place

The Fano plane is the projective plane over the finite field F 2\mathbf{F}_2 with two elements. It is denoted either 𝔽 2 2\mathbb{F}_2\mathbb{P}^2, 𝔽 2 2\mathbb{P}^2_{\mathbb{F}_2} (in algebraic geometry), or PG(2,2)PG(2,2) (in finite geometry). It is often pictured as at right, but there are many different representations.

Properties

Automorphisms

The automorphism group PGL(3,𝔽 2)PGL(3,\mathbb{F}_2) is isomorphic to the projective special linear group PSL(2,𝔽 7)PSL(2,\mathbb{F}_7).

References

Last revised on December 2, 2016 at 04:57:32. See the history of this page for a list of all contributions to it.