Unitals and replaceable t-nests

Replaceable Nests

Non-Existence of isomorphisms between certain unitals

We show that the Ree-Tits unitals are neither classical nor isomorphic to the polar unitals found in the Coulter-Matthews planes. To this end, we determine the full automorphism groups of the (finite) Ree unitals.

An alternative construction of B-M and B-T unitals in desarguesian planes

We present a new construction of non-classical unitals from a classical unital U in PG(2, q2). The resulting non-classical unitals are B-M unitals. The idea is to find a non-standard model Π of PG(2, q2) with the following three properties: (i) points of Π are those of PG(2, q2); (ii) lines of Π are certain lines and conics of PG(2, q2); (iii) the points in U form a non-classical B-M unital in ...

Constructions of unitals in Desarguesian planes

We present a new construction of non-classical unitals from a classical unital U in PG(2, q2). The resulting non-classical unitals are B–M unitals. The idea is to find a non-standard model Π of PG(2, q2) with the following three properties: (i) points of Π are those of PG(2, q2); (ii) lines of Π are certain lines and conics of PG(2, q2); (iii) the points in U form a non-classical B–M unital in ...

On deriving unitals

We provide short proofs that suitable unitals in derivable projective planes give rise to unitals in the derived planes, Some known constructions of unitals in Hall planes are immediate corollaries. @ 1999 Elsevier Science B.V. All rights reserved