✦ LIBER ✦

On the Number of Planes in Neumaier's A8-Geometry

✍ Scribed by Philippe Cara

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 55 KB
Volume: 93
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3073

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✦ Synopsis

In one of his papers [2], A. Neumaier constructed a rank 4 incidence geometry on which the alternating group of degree 8 acts flag-transitively. This geometry is quite important since its point residue is the famous A 7 -geometry which is known to be the only flag-transitive locally classical C 3 -geometry which is not a polar space (see [1]). By counting chambers, we prove that the A 8 -geometry has 70 planes. This can be found in a paper of Pasini's [4] without proof, but Neumaier's original paper only mentions 35 planes.

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