## Lectures on Projective PlanesDepartment of Mathematics, University of Illinois at Chicago Circle, 1969 - Geometry, Plane |

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### Contents

SOME GENERAL RESULTS DESARGUESIAN | 1-1 |

4 Perspectivities 1 | 1-9 |

5 Desargues Postulate 1 | 1-18 |

7 other sections not shown

### Common terms and phrases

a,b e absolute points affine plane alternative field assume axis central collineation collinear collineation group collineation of TT congruence partition contains Corollary define definition denote desarguesian plane different points elements exists finite projective plane fixed line fixed points Furthermore GF(q group of TT Hence homology with center hypothesis implies incidence matrix incidence structure induces integer involution involutory homology isomorphism Lemma Let G Let TT line of TT n-set near-field plane non-centers non-trivial elation non-trivial homology number of point permutation group permutation matrix plane of order plane with respect point orbits point-line pair points of TT pointwise postulate prime Proof Proposition quadrangle quasi-field rank set of points subgroup subplane Sylow 2-subgroup tactical configuration tactical decomposition tangents ternary field Theorem translation plane TT is desarguesian TT(G TT(V unique vector space