The classification of spreads in PG(3, q) admitting linear groups of order q( q+1), I. odd order.

A classification is given of all spreads in PG(3, q), q = p r, p odd, whose associated translation planes admit linear collineation groups of order q( q +1) such that a Sylow p-subgroup fixes a line and acts non-trivially on it. [ABSTRACT FROM AUTHOR]