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Affine Distance-transitive Groups of Dimension One

✍ Scribed by Arjeh M. Cohen; Alexander A. Ivanov

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 77 KB
Volume: 21
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0277

No coin nor oath required. For personal study only.

✦ Synopsis

containing the translations and acting primitively on the set of vectors in V . Let G 0 be the stabilizer in G of the zero vector, so that G 0 ≤ L(V ) ∼ = L(1, q) and G = V : G 0 . Suppose that is a graph structure on V on which G acts distance-transitively. Such graphs of diameter at most 2 are known from the literature. Here, we show that if has diameter at least 3, then q = 64, G 0 ∼ = Z 9 : Z 3 or Z 9 : Z 6 and is the Hamming graph H (4, 3).

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