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On the order of arc-stabilisers in arc-transitive graphs with prescribed local group


Authors: Primož Potočnik, Pablo Spiga and Gabriel Verret
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
Published electronically: March 14, 2014
MathSciNet review: 3192615
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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 $ \vert G_{uv}\vert$ 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
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

DOI: https://doi.org/10.1090/S0002-9947-2014-05992-8
Keywords: Arc-transitive graphs, arc-stabiliser, graph-restrictive group, local group.
Received by editor(s): July 24, 2012
Received by editor(s) in revised form: October 10, 2012
Published electronically: March 14, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.