Geodesic
A Family of Unitals in the Hughes Plane
Canadian journal of mathematics, Tome 42 (1990) no. 6, pp. 1067-1083

Voir la notice de l'article provenant de la source Cambridge University Press

We construct a family of unitals in the Hughes plane. We prove that they are not isomorphic with the classical unitals, and in so doing we exhibit a configuration that exists in the latter, but not in the former. This new configurational property of the classical unitals might serve in the future again as an isomorphism test.A particular instance of our construction has appeared in [11]. But it only concerns itself with the case where the matrix involved is the identity, whereas the present article treats the general case of symmetric matrices over a suitable field. Furthermore, [11] does not answer the isomorphism question. It states that (the English translation is ours) “It remains to be seen whether the unitary designs constructed in this note are isomorphic or not with known designs”.
DOI : 10.4153/CJM-1990-057-1
Mots-clés : 51E20, 05B30 
Kestenband, Barbu C. A Family of Unitals in the Hughes Plane. Canadian journal of mathematics, Tome 42 (1990) no. 6, pp. 1067-1083. doi: 10.4153/CJM-1990-057-1
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