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Affine distance-transitive graphs with quadratic forms

Published online by Cambridge University Press:  24 October 2008

John Van Bon
John Van Bon
Affiliation:
Department of Mathematics, Tufts University, Medford, MA 02155, U.S.A.
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Extract

The classification of all finite primitive distance-transitive graphs is basically divided into two cases. In the one case, known as the almost simple case, we have an almost simple group acting primitively as a group of automorphisms on the graph. In the other case, known as the affine case, the vertices of the graph can be identified with the vectors of a finite-dimensional vector space over some finite field. In this case the automorphism group G of the graph Γ contains a normal p-subgroup N which is elementary Abelian and acts regularly on the set of vertices of Γ. Let G0 be the subgroup of G that stabilizes a vertex. Identifying the vertices of Γ with G0-cosets in G, one obtains a vector space V on which N acts as a group of translations, G0, stabilizes 0 and, as Γ is primitive, G0 acts irreducibly on V.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 3 , November 1992 , pp. 507 - 517
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

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