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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

Published online by Cambridge University Press:  24 August 2009

V. I. TROFIMOV
V. I. TROFIMOV*
Affiliation:
Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Branch, 620219 Ekaterinburg, Russia. e-mail: trofimov@imm.uran.ru
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 1 , January 2010 , pp. 33 - 45
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

REFERENCES

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