On the embedding of some linear spaces in finite projective planes (Q1581010)

The problem of embedding of linear spaces in finite projective planes has been examinated by several authors. In particular, it has been proved that a linear space which is the complement of a projective or affine subplane of order \(m\) is embeddable in a unique way in a projective plane of order \(n\). In this paper, the authors give a generalization of this result by embedding linear spaces in a finite projective plane of order \(n\), with \(2\leq m\), \(n\), which are complements of certain regular \(A\)-affine linear spaces with respect to a finite projective plane. The details are too involved to be described here.