Abstract projective plane

Fano plane

The Fano plane is an Abstract projective plane and Galois geometry PG(2,2) =P(ℤ32). fin In addition it forms the unique Steiner system S⁡(2,3,7), where lines are triads.

The Fano plane is shares an intimate relationship with the Binary 7,4,3 Hamming code.

Properties

  • PGL⁡(3,2) ≅PGL⁡(1,7)1

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Footnotes

  1. 1988. Geometry of the Mathieu groups and Golay codes ↩

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