ABSTRACT
Concerning the possibility of partitions of projective geometries, A.A. Bruen and J.A. Thas [198] determined that it is possible to construct partitions of the points of PG(2s− 1, q2) by projective subgeometries isomorphic to PG(s− 1, q2)’s and PG(2s − 1, q)’s. Since there are at least two possible types of geometries such partitions perhaps could be called ‘mixed subgeometry partitions’. Bruen and Thas showed that there is an associated translation plane of order q2s and kernel containing GF (q), to contrast with a construction using Segre varieties. That is, a more general construction using Segre varieties is given in Hirschfeld and Thas [529], which generalizes the previously mentioned results of Bruen and Thas and includes Baer subgeometry partitions of PG(2s, q2) by PG(2s, q)’s. In this latter case, there is an associated translation plane of order q2s+1 and kernel containing GF (q).
