ABSTRACT
Every translation plane may be obtained by a net replacement applied to a Desarguesian plane, and the simplest type of finite replaceable net corresponds to regulus replacements. Moreover disjoint unions of nets, hence disjoint unions of reguli, are themselves replaceable. So a basic area of study are the planes obtainable by deriving simultaneously the reguli in any collection of pairwise disjoint reguli, of a Desarguesian line spread in PG(3, q): such spreads are subregular spreads, obtained by ‘multiply deriving’ a Desarguesian spread. Thus, the two-dimensional Andre´ planes are always subregular, and these are the only generalized Andre´ planes that are subregular (since prime-dimensional λ-planes are Andre´ planes).
