Projective planar spaces (Q811817)

A planar space is a triple \((\mathcal S, \mathcal L,\mathcal P)\), where \((\mathcal S,\mathcal L)\) is a linear space and \({\mathcal P}\) is a set of proper subspaces of \({\mathcal L}\), called planes, such that any three non-collinear points lie in a unique plane and every plane contains three non-collinear points. In the paper under review the author proves that \((\mathcal S,\mathcal L)\) is a projective space if and only if there exists an \(a \in S\) such that all planes through \(a\) are projective planes.