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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
Affiliation:
Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Branch, 620219 Ekaterinburg, Russia. e-mail: trofimov@imm.uran.ru
Corresponding
E-mail address:

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
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

[1]McLaughlin, J.Some subgroups of SLn(F 2). Ill. J. Math. 13 (1969), 108115.Google Scholar
[2]Meierfrankenfeld, U. Eine Lösung des Pushing-up Problems für eine Klasse endlicher Gruppen. Dissertation (Universität Bielefeld, 1986).Google Scholar
[3]Trofimov, V. I.Graphs with projective suborbits. Exceptional cases of characteristic 2. I (in Russian). Izv. Ross. Akad. Nauk: Ser. Mat. 62 (1998), no. 6, 159222; translation in Izv. Math. 62 (1998), no. 6, 1221–1279.Google Scholar
[4]Trofimov, V. I.Graphs with projective suborbits. Exceptional cases of characteristic 2. III (in Russian). Izv. Ross. Akad. Nauk: Ser. Mat. 65 (2001), no. 4, 151190; translation in Izv. Math. 65 (2001), no. 4, 787–822.Google Scholar
[5]Trofimov, V. I. and Weiss, R. M. The group E 6(q) and graphs with a locally linear group of automorphisms. Math. Proc. Cambridge Phil. Soc., this issue.Google Scholar

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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
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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
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