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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Graphs with subconstituents containing $L_{3}(p)$
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by Richard Weiss PDF
Proc. Amer. Math. Soc. 85 (1982), 666-672 Request permission

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
  • © Copyright 1982 American Mathematical Society
  • 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