Enumeration of orthogonal Buekenhout unitals

Enumeration of Nonsingular Buekenhout Unitals

The only known enumeration of Buekenhout unitals occurs in the Desarguesian plane PG(2, q2). In this paper we develop general techniques for enumerating the nonsingular Buekenhout unitals embedded in any two-dimensional translation plane, and apply these techniques to obtain such an enumeration in the regular nearfield planes, the odd-order Hall planes, and the flag-transitive affine planes. We...

Group theoretic characterizations of Buekenhout – Metz unitals in PG ( 2 , q 2 )

Let G be the group of projectivities stabilizing a unital U in PG(2, q2) and let A,B be two distinct points of U . In this paper we prove that, if G has an elation group of order q with center A and a group of projectivities stabilizing both A and B of order a divisor of q − 1 greater than 2(√q − 1), then U is an ovoidal Buekenhout–Metz unital. From this result two group theoretic characterizat...

Buekenhout-Tits Unitals

A Buekenhout-Tits unital is defined to be a unital in PG(2, q2) obtained by coning the Tits ovoid using Buekenhout’s parabolic method. The full linear collineation group stabilizing this unital is computed, and related design questions are also addressed. While the answers to the design questions are very similar to those obtained for Buekenhout-Metz unitals, the group theoretic results are qui...

Buekenhout unitals

A class of Buekenhout unitals in the Hall plane

Let U be the classical unital in PG(2, q2) secant to `∞. By deriving PG(2, q) with respect to a derivation set disjoint from U we obtain a new unital U ′ in the Hall plane of order q2. We show that this unital contains O’Nan configurations and is not isomorphic to the known unitals of the Hall plane, hence it forms a new class of unitals in the Hall plane.