Thenon-solvable triangle transitive planes

The class of finite translation planes admitting non-solvable triangle transitive groups is completely determined as the class of irregular nearfield planes admitting non-solvable groups

Classification of flocks of the quadratic cone in PG(3,64)

Flocks are an important topic in the field of finite geometry, with many relations with other objects of interest. This paper is a contribution to the difficult problem of classifying flocks up to projective equivalence. We complete the classification of flocks of the quadratic cone in PG(3,q) for q ≤ 71, by showing by computer that there are exactly three flocks of the quadratic cone in PG(3,64), up to equivalence. The three flocks had previously been discovered, and they are the linear flock, the Subiaco flock and the Adelaide flock. The classification proceeds via the connection between flocks and herds of ovals in PG(2,q), q even, and uses the prior classification of hyperovals in PG(2, 64)

Homology groups of translation planes and flocks of quadratic cones, II; j-planes

The set of j-planes with spreads in PG(3,K), for K a field admitting a quadratic field extension K+ is shown to be equivalent to the set of all det K+-monomial partial flocks of a quadratic cone. Using this connection, when K is GF(2r), the set of j-planes is determined and j = 0, 1, or 2 and correspond to the linear, Walker/Betten or Payne conical flocks, respectively. When K is the field of real numbers, the set of j-planes is completely determined and j is any real number > -&#x00BD

Hemisystems of small flock generalized quadrangles

In this paper, we describe a complete computer classification of the hemisystems in the two known flock generalized quadrangles of order $(5^2,5)$ and give numerous further examples of hemisystems in all the known flock generalized quadrangles of order $(s^2,s)$ for $s \le 11$. By analysing the computational data, we identify two possible new infinite families of hemisystems in the classical generalized quadrangle $H(3,q^2)$.Comment: slight revisions made following referee's reports, and included raw dat