Frobenius collineations in finite projective planes (Q1281189)

The author studies a special class of collineations of finite Desarguesian projective planes, which he calls Frobenius collineations. For \(q\equiv 2\pmod 3\), the Singer cycles of \(\text{PG}(2,q^2)\) induce a rank 2 geometry on the Baer subplanes of \(\text{PG}(2,q^2)\) fixed by a given Frobenius collineation. The author calls this rank 2 geometry a Frobenius plane of order \(q\). He also constructs a related rank 3 geometry, which he calls a Frobenius space of order \(q\). He studies the properties of Frobenius planes and spaces.