ABSTRACT
In this chapter, we provide statements of results used in the proof of the following classi…cation theorem, as well as in other results on translation planes and t-spreads.
Theorem 284. Let P be a de…ciency one parallelism in PG(3; q) that admits a collineation group in PL(4; q) acting transitively on the spreads of the partial parallelism. Let P denote the unique extension of P to a parallelism. Let the …xed spread be denoted by 0 (the ‘socle’) and let the remaining q2 + q spreads of P be denoted by i, for i = 1; 2; ::; q2 + q. Let i denote the a¢ ne translation plane corresponding to i. Then 0 is Desarguesian and i is a derived conical ‡ock plane for i = 1; 2; ::; q2 + q.
