ABSTRACT
In the previous chapter, we have seen that there exist derivable nets in nonderivable affine planes. The affine planes in question are dual translation planes. Could such a plane be a translation plane? Note that when i f is a field in the above context then a derivable net corresponds to a regulus in some projective space isomorphic to P G (3 ,if). So, we have a non-derivable extension plane of a regulus net. However, the plane does not necessar ily correspond to a spread of PG(3, if). Thus, we arrive at the following question:
G iven a regulus R in P G (3 ,if), for i f a field, assum e th a t th e re is a sp read in P G (3 ,if) which contains i?. Is th e corresponding tran sla tio n p lane derivable?
