Abstract
By deriving the desarguesian plane of order q2 for every prime power q a unital of order q is constructed which can be embedded in both the Hall plane and the dual of the Hall plane of order q2 which are non-isomorphic projective planes. The representation of translation planes in the fourdimensional projective space of J. André and F. Buekenhouts construction of unitals in these planes are used. It is shown that the full automorphism groups of these unitals are just the collineation groups inherited from the classical unitals.
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References
André, J.: Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe. Math. Zeitschr. 60 (1954), 156–186
Brouwer, A. E.: Some unitals on 28 points and their embeddings in projective planes of order 9. Math. Centre Report ZW155 (1981)
Buekenhout, F.: Existence of Unitals in Finite Translation Planes of order q2 with a kernel of Order q. Geometriae Dedicata 5 (1976), 189–194
Dembowski, P.: Finite Geometries. Berlin-Heidelberg-New York (1968)
O'Nan, M.: Automorphisms of Unitary Block Designs. J. Algebra 20 (1972), 495–511
Piper, F.: Unitary Block Designs. Grap Theory and Combinatorics (R. J. Wilson ed.), Research Notes in Mathematics 34
Tallini Scafati, M.: Sui {k,n}-archi in un piano grafico finito, con particolare riguardo a quelli con due caratteri. Rend. Acc. Nat. Lincei 8 (1966), 812–818, 1020–1025
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Grüning, K. A class of unitals of order q which can be embedded in two different planes of order q2 . J Geom 29, 61–77 (1987). https://doi.org/10.1007/BF01234988
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DOI: https://doi.org/10.1007/BF01234988