Fano Configurations in Subregular Planes

Abstract

In this article a wide variety of odd-order translation planes, constructedfrom Desarguesian planes by multiple derivation, are shown to admit Fanoconfigurations. For example, we show that subregular planes of odd order obtained by the replacement of at most disjoint nets admitFano configurations. Further, for odd and greater than 1, any subregularplane of order can be embedded into a subregular plane of order that contains the original plane as a subplane and admits Fano configurations.