Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



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
Published electronically: March 14, 2014
MathSciNet review: 3192615
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $\Gamma$.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 20B25, 05E18

Retrieve articles in all journals with MSC (2010): 20B25, 05E18

Additional Information

Primož Potočnik
Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia

Pablo Spiga
Affiliation: Departimento di Matematica Pura e Applicata, University of Milano-Bicocca, Via Cozzi 53, 20126 Milano, Italy
MR Author ID: 764459

Gabriel Verret
Affiliation: Faculty of Mathematics, Natural Sciences and Information Technology, University of Primorska, Glagoljaška 8, 6000 Koper, Slovenia

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.