Collineations and Generalized Incidence Matrices

DOI10.2307/1993015zbMath0078.34102OpenAlexW4253076612MaRDI QIDQ3245702

Daniel Hughes

Publication date: 1957

Full work available at URL: https://doi.org/10.2307/1993015

zbMATH Keywords

collineation groupgeneralized incidence matricesMinkowski-Hasse theorynonexistence theorems for finite projective planesrational congruence

Mathematics Subject Classification ID

Finite affine and projective planes (geometric aspects) (51E15) Topological linear incidence structures (51H10)

Related Items

Elations of finite projective planes ⋮ Quadratische Formen und Kollineationsgruppen ⋮ Projective extensions of Kirkman systems as substructures of projective planes ⋮ Finite planes with a single (p, L) transitivity ⋮ Collineations of projective planes of order 10. Part I ⋮ Groups of projective planes with differing numbers of point and line orbits ⋮ Planes of order 10 do not have a collineation of order 5 ⋮ Codes and designs ⋮ On partitions and permutation groups on unordered sets ⋮ Matrices of zeros and ones ⋮ On representing block designs in terms of their automorphisms ⋮ Planes of order \(n\) with collineation groups of order \(n^ 2\) ⋮ On the orbits of collineation groups ⋮ Automorphism groups of designs ⋮ On collineation groups of symmetric block designs ⋮ On perspectivities of finite projective planes ⋮ On projective and affine planes with transitive collineation groups ⋮ A theorem on finite projective planes of odd order and an application to planes of order 15 ⋮ Automorphism groups of graphs ⋮ Tactical decompositions of designs ⋮ On abelian projective planes ⋮ On the construction of finite projective planes from homology semibiplanes ⋮ Collineation groups which are sharply transitive on an oval

Cites Work

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• Planar Division Neo-Rings
• Partial Difference Sets
• Regular Collineation Groups
• Combinatorial Problems
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• A Note on a Combinatorial Problem
• Cyclic Incidence Matrices
• Matrices with Integer Elements in Combinatorial Investigations
• Cyclic Affine Planes
• Projective Planes
• Projectivities with fixed points on every line of the plane
• Difference Sets in a Finite Group