## Projective planes |

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### Contents

Review of Basic Algebra | 5 |

Classical Projective Planes | 17 |

Elementary Properties of Projective and Affine Planes | 76 |

Copyright | |

40 other sections not shown

### Common terms and phrases

3-incident abelian absolute points affine plane affine points algebra arbitrary automorphism autotopism axis Baer subplane Bruck-Ryser Theorem centre Chapter Clearly closed configuration collinear conic contains coordinates coordinatized cross-ratio define desarguesian plane dimension distinct points division ring plane dual elation equation exactly field finite field finite projective plane fixes free closures free extension Frobenius group g-dimension GF(q given gives Hall plane harmonic conjugate Hence homomorphism identity implies incident induces intersection involutory involutory homology isomorphic kernel latin squares left vector space Lemma line joining linear transformation matrix non-singular non-trivial non-zero number of points orbit orthogonal permutation group perspectivity PGL(V planar ternary rings plane of order points and lines polarity projective geometry Proof properties prove Q Corollary Q Exercise quasifield Result satisfies semi-linear transformation set of points Singer group skewfield subgroup subspaces Suppose Theorem translation plane triangle unique solution