Translation planes of order q3 which admits SL(2, q)

ON TRANSLATION PLANES OF ORDER q WHICH ADMIT AN AUTOTOPISM GROUP HAVING AN ORBIT OF LENGTH q-q

The Translation Planes of Order Twenty-Five

The purpose of this paper is to classify the translation planes of order twenty-five. Andre [l] and Bruck and Bose [3] have shown there is a one-one correspondence between spreads in projective space and translation planes. We use this fact to classify the spreads in the three-dimensional projective space PG(3, q). The translation planes of order 16 have been classified by Dempwolff and Reifart...

Translation planes admitting a linear Abelian group of order (q+1)2

Translation planes of order q and spread in PG(3, q), where q is an odd prime power and q− 1 has a p-primitive divisor, that admit a linear Abelian group of order (q + 1) containing at most three kernel homologies are shown to be associated to flocks of quadratic cones.

NESTS OF SIZE q-\ AND ANOTHER FAMILY OF TRANSLATION PLANES

We define a nest of reguli to be a collection P of reguli in a regular spread S of PG(3, q) such that every line of S is contained in exactly zero or two reguli of P. This generalizes the notion of a chain of reguli first introduced by Bruen. If U denotes the lines of S contained in the reguli of P and V is a partial spread of PG(3, q) covering the same points as U, then (S\U) U Vis a spread of...

Sixteen-dimensional Locally Compact Translation Planes Admitting Sl2 H as a Group of Collineations

In this paper, all 16-dimensional locally compact translation planes admitting the unimodular quaternion group SL2H as a group of collineations will be determined explicitly. Besides the classical plane over the octonions there are a vast number of planes having this property, cf. the Classification Theorem (2.8). Indeed, the class of these planes covers an interesting borderline case: Among al...