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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Graphs with subconstituents containing $ L\sb{3}(p)$


Author: Richard Weiss
Journal: Proc. Amer. Math. Soc. 85 (1982), 666-672
MSC: Primary 05C25; Secondary 20B25
MathSciNet review: 660626
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Abstract: Let $ \Gamma $ be a finite connected undirected graph, $ G$ a vertex-transitive subgroup of $ \operatorname{aut} (\Gamma )$, $ \{ x,y\} $ an edge of $ \Gamma $ and $ {G_i}(x,y)$ the subgroup of $ G$ fixing every vertex at a distance of at most $ i$ from $ x$ or $ y$. We show that if the stabilizer $ {G_x}$ contains a normal subgroup inducing $ {L_3}(p)$, $ p$ a prime, on the set of vertices adjacent to $ x$, then $ {G_5}(x,y) = 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660626-6
PII: S 0002-9939(1982)0660626-6
Keywords: Symmetric graph, projective plane
Article copyright: © Copyright 1982 American Mathematical Society