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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the order of arc-stabilisers in arc-transitive graphs with prescribed local group
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by Primož Potočnik, Pablo Spiga and Gabriel Verret PDF
Trans. Amer. Math. Soc. 366 (2014), 3729-3745 Request permission

Abstract:

Let $\Gamma$ be a connected $G$-arc-transitive graph, let $uv$ be an arc of $\Gamma$ and let $L$ be the permutation group induced by the action of the vertex-stabiliser $G_v$ on the neighbourhood $\Gamma (v)$. We study the problem of bounding $|G_{uv}|$ in terms of $L$ and the order of $\Gamma$.
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Additional Information
  • Primož Potočnik
  • Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
  • Email: primoz.potocnik@fmf.uni-lj.si
  • Pablo Spiga
  • Affiliation: Departimento di Matematica Pura e Applicata, University of Milano-Bicocca, Via Cozzi 53, 20126 Milano, Italy
  • MR Author ID: 764459
  • Email: pablo.spiga@unimib.it
  • Gabriel Verret
  • Affiliation: Faculty of Mathematics, Natural Sciences and Information Technology, University of Primorska, Glagoljaška 8, 6000 Koper, Slovenia
  • Email: gabriel.verret@pint.upr.si
  • Received by editor(s): July 24, 2012
  • Received by editor(s) in revised form: October 10, 2012
  • Published electronically: March 14, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 3729-3745
  • MSC (2010): Primary 20B25; Secondary 05E18
  • DOI: https://doi.org/10.1090/S0002-9947-2014-05992-8
  • MathSciNet review: 3192615