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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:automorphismGroup
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gptkb:projective_linear_group
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gptkbp:definedIn
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finite fields
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gptkbp:dimensions
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n-dimensional
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gptkbp:example
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gptkb:Fano_plane
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gptkbp:field
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gptkb:combinatorics
gptkb:geometry
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gptkbp:generalizes
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projective planes
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gptkbp:has_lines
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finite set
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gptkbp:has_points
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finite set
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gptkbp:notation
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PG(n,q)
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gptkbp:number_of_lines_in_PG(2,q)
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q^2+q+1
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gptkbp:number_of_points_in_PG(n,q)
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(q^{n+1}-1)/(q-1)
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gptkbp:order
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q (a prime power)
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gptkbp:property
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homogeneous coordinates
no parallel lines
any two distinct lines meet in a unique point
any two distinct points determine a unique line
duality principle applies
every line contains q+1 points
every point lies on q+1 lines
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gptkbp:relatedTo
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gptkb:geometry
gptkb:Galois_fields
incidence structures
block designs
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gptkbp:studiedBy
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gptkb:geometry
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gptkbp:used_in
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coding theory
design theory
finite group theory
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gptkbp:bfsParent
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gptkb:Bose–Burton_theorem
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gptkbp:bfsLayer
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8
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https://www.w3.org/2000/01/rdf-schema#label
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finite projective spaces
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