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Inverse planes with a given collection of common blocks

✍ Scribed by G.L. Ebert

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 736 KB
Volume: 131
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90374-3

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✦ Synopsis

It is well known that it is possible to construct ($-q)/2 (miquelian) inversive planes of order q on the same set of points which pairwise intersect in precisely the circles through infinity. Here we give an explicit description of such a family by "projecting" certain Buekenhout-Metz unitals in a well-defined manner. If q > 8 is an odd power of 2, it is shown that an additional q2 -q (Suzuki-Tits) inverse planes may be added to the family without disturbing the above intersection property. The maximal&y of the resulting families is then discussed.

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