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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Graphs with automorphism groups admitting composition factors of bounded rank


Authors: Cheryl E. Praeger, Laszló Pyber, Pablo Spiga and Endre Szabó
Journal: Proc. Amer. Math. Soc. 140 (2012), 2307-2318
MSC (2000): Primary 20B25
Published electronically: November 23, 2011
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Abstract: We prove a $ 1978$ conjecture of Richard Weiss in the case of groups with composition factors of bounded rank. Namely, we prove that there exists a function $ g: \mathbb{N} \times \mathbb{N} \to \mathbb{N}$ such that, for $ \Gamma $ a connected $ G$-vertex-transitive, $ G$-locally primitive graph of valency at most $ d$, if $ G$ has no alternating groups of degree greater than $ r$ as sections, then a vertex stabiliser in $ G$ has size at most $ g(r,d)$.


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Additional Information

Cheryl E. Praeger
Affiliation: Centre for Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia
Email: praeger@maths.uwa.edu.au

Laszló Pyber
Affiliation: Rényi Institute of Mathematics, Hungarian Academy of Sciences, P. O. Box 127, H-1364 Budapest, Hungary
Email: pyber@renyi.hu

Pablo Spiga
Affiliation: Centre for Mathematics of Symmetry and Computation, School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia
Email: spiga@maths.uwa.edu.au

Endre Szabó
Affiliation: Rényi Institute of Mathematics, Hungarian Academy of Sciences, P. O. Box 127, H-1364 Budapest, Hungary
Email: endre@renyi.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11100-6
PII: S 0002-9939(2011)11100-6
Keywords: Weiss conjecture, normal quotients, quasiprimitive groups, almost simple groups
Received by editor(s): December 16, 2010
Received by editor(s) in revised form: January 12, 2011, and February 28, 2011
Published electronically: November 23, 2011
Additional Notes: The first author is supported by the ARC Federation Fellowship Project FF0776186.
The second author is supported in part by OTKA 78439 and 72523.
The third author is supported by the University of Western Australia as part of the Federation Fellowship project.
The fourth author is supported in part by OTKA 81203 and 72523.
Dedicated: For the 60th birthday of L. Babai
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2011 American Mathematical Society