Subplane of projective plane

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Template:Projective plane-subset property

Definition

A subplane of a projective plane is a subset of the point and line set that becomes a projective plane with the induced incidence structure. In other words:

  • If two points belong to the subset, so does the line incident with them
  • If two lines belong to the subset, so does the point incident with them
  • The subset contains a quadrangle

Relation with other properties

Weaker properties