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

Bol planes of orders 3434 and 3636

Finite Bol planes of order not $34$ or $36$ are known to be nearfield planes. This article resolves the remaining cases; Finite Bol planes are nearfield

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

Infinite hyper-regulus Sperner spaces

New constructions of infinite hyper-reguli are given, which produce a variety of new translation planes and Sperner spaces