Affine Distance-transitive Graphs with Sporadic Stabilizer

✍ Scribed by J. van Bon; A.A. Ivanov; J. Saxl

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 215 KB
• Volume: 20
• Category: Article
• ISSN: 0195-6698
• DOI: 10.1006/eujc.1998.0268

✦ Synopsis

This paper is a contribution to the programme to classify finite distance-transitive graphs and their automorphism groups. We classify pairs ( , G) where is a graph and G is an automorphism group of acting distance-transitively and primitively on the vertex set of , subject to the condition that there is a normal elementary abelian subgroup V in G which acts regularly on the vertex set of and the stabilizer G 0 of a vertex (which is a complement to V in G) has a unique non-abelian composition factor isomorphic to one of the 26 sporadic simple groups. There are exactly 10 examples of , all known for a long time.