ABSTRACT
When we studied tangentially transitive translation planes, it was shown that either the plane has order 16 or the plane is always derivable and the derived plane is a semifield plane with the ‘middle-nucleus property’. That is, the plane may be coordinatized by a semifield of order q2 with its middle nucleus isomorphic to GF(q). In this case, the subplane π0, with which the group is tangentially transitive, has order q. When the order is 16, it is still true that the plane is derivable and there is a subplane of order 4, with which there is a tangentially transitive group H. But, here more is true, there is also a subplane of order 2 and a group G D H that is tangentially transitive with respect to this smaller subplane. In this setting, the group is isomorphic to PSL(2,7) ~ PGL(3,2).
