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: ℕ × ℕ → ℕ such that, for Γ 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). © 2011 American Mathematical Society.
Praeger, C., Pyber, L., Spiga, P., Szabó, E. (2012). Graphs with automorphism groups admitting composition factors of bounded rank. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 140(7), 2307-2318 [10.1090/S0002-9939-2011-11100-6].
Graphs with automorphism groups admitting composition factors of bounded rank
SPIGA, PABLOPenultimo
;
2012
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: ℕ × ℕ → ℕ such that, for Γ 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). © 2011 American Mathematical Society.
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