Projective Planes |
Contents
viii | 2 |
Classical Projective Planes | 4 |
Elementary Properties of Projective and Affine Planes | 11 |
Copyright | |
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A₁ abelian absolute points affine plane algebraic aẞ automorphism autotopism axis B₁ Baer subplane Bruck-Ryser Theorem centre Chapter Clearly collinear collineation group configuration conic contains coordinatized Corollary cross-ratio define desarguesian plane dimension distinct points division ring division ring plane e₁ E₂ elation equation Exercise field finite field finite projective plane fixes g-dimension GF q given gives Hence homology homomorphism identity implies incident induces intersection involutory isomorphic k)-transitivity k₂ kernel latin squares left vector space Lemma line joining linear transformation matrix non-singular orbit orthogonal P₁ P₂ permutation group perspectivity PGL(V planar ternary rings plane of order points and lines polarity projective geometry Proof properties prove quasifield Result satisfies semi-linear transformation set of points Singer group skewfield subgroup subspaces Suppose Theorem transitive translation plane triangle unique solution W₁ W₂