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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Graphs with subconstituents containing $L_{3}(p)$


Author: Richard Weiss
Journal: Proc. Amer. Math. Soc. 85 (1982), 666-672
MSC: Primary 05C25; Secondary 20B25
DOI: https://doi.org/10.1090/S0002-9939-1982-0660626-6
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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Keywords: Symmetric graph, projective plane
Article copyright: © Copyright 1982 American Mathematical Society