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

A Census Of Highly Symmetric Combinatorial Designs

As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v,k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t > 2 most of these characterizations have remained longstanding challenging problems. Especially, the determination of all flag-transitive Steiner t-designs with 2 < t < 7 is of particular interest and has been open for about 40 years (cf. [11, p. 147] and [12, p. 273], but presumably dating back to 1965). The present paper continues the author's work [20, 21, 22] of classifying all flag-transitive Steiner 3-designs and 4-designs. We give a complete classification of all flag-transitive Steiner 5-designs and prove furthermore that there are no non-trivial flag-transitive Steiner 6-designs. Both results rely on the classification of the finite 3-homogeneous permutation groups. Moreover, we survey some of the most general results on highly symmetric Steiner t-designs.Comment: 26 pages; to appear in: "Journal of Algebraic Combinatorics

Large quartic groups on translation planes, III-groups with common centers

The 'desirable' planes odd order of Biliotti, Jha, Johnson, Menichetti are shown to be exactly the class of planes that admit two trivially intersecting quartic groups of order q with common centers

Lorentz Dynamics on Closed 3-Manifolds

In this paper, we give a complete topological, as well as geometrical classification of closed 3-dimensional Lorentz manifolds admitting a noncompact isometry group

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