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Supplement to 'The group E6(q) and graphs with a locally linear group of automorphisms' by V. I. Trofimov and R. M. Weiss
- Source :
- Mathematical Proceedings of the Cambridge Philosophical Society. 148:33-45
- Publication Year :
- 2009
- Publisher :
- Cambridge University Press (CUP), 2009.
-
Abstract
- Let q be a prime power and let G be a group acting faithfully and vertex transitively on a graph such that for each vertex x, the stabilizer Gx is finite and contains a normal subgroup inducing on the set of neighbours of x a permutation group isomorphic to the linear group L5(q) acting on the 2-dimensional subspaces of a 5-dimensional vector space over Fq. In a companion paper, it is shown, except in some special situations where q = 2, that the kernel of the action of a vertex stabilizer Gx on the ball of radius 3 around x is trivial. In this paper we show that these special situations cannot occur.
Details
- ISSN :
- 14698064 and 03050041
- Volume :
- 148
- Database :
- OpenAIRE
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Accession number :
- edsair.doi...........6277a39b6c9c150d36d537d57947115a