Baer Partitions of Small Order Projective Planes

Abstract

The partitions into Baer subplanes of the Desarguesian projective planes of order $9$, $16$, and $25$ are classified by computer. It is also shown that the non-Desarguesian projective planes of order $9$ and the non-Desarguesian translation planes of order $16$ and $25$ do not admit such a partition.