Graphs with automorphism groups admitting composition factors of bounded rank

Praeger, Cheryl; Pyber, Laszló; Spiga, Pablo; Szabó, Endre

doi:10.1090/S0002-9939-2011-11100-6

Graphs with automorphism groups admitting composition factors of bounded rank
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by Cheryl E. Praeger, Laszló Pyber, Pablo Spiga and Endre Szabó

Proc. Amer. Math. Soc. 140 (2012), 2307-2318

DOI: https://doi.org/10.1090/S0002-9939-2011-11100-6

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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