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- W2949274727 abstract "In this paper we discuss a method for bounding the size of the stabiliser of a vertex in a $G$-vertex-transitive graph $Gamma$. In the main result the group $G$ is quasiprimitive or biquasiprimitive on the vertices of $Gamma$, and we obtain a genuine reduction to the case where $G$ is a nonabelian simple group. Using normal quotient techniques developed by the first author, the main theorem applies to general $G$-vertex-transitive graphs which are $G$-locally primitive (respectively, $G$-locally quasiprimitive), that is, the stabiliser $G_alpha$ of a vertex $alpha$ acts primitively (respectively quasiprimitively) on the set of vertices adjacent to $alpha$. We discuss how our results may be used to investigate conjectures by Richard Weiss (in 1978) and the first author (in 1998) that the order of $G_alpha$ is bounded above by some function depending only on the valency of $Gamma$, when $Gamma$ is $G$-locally primitive or $G$-locally quasiprimitive, respectively." @default.
- W2949274727 created "2019-06-27" @default.
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- W2949274727 date "2011-02-08" @default.
- W2949274727 modified "2023-09-27" @default.
- W2949274727 title "Bounding the size of a vertex-stabiliser in a finite vertex-transitive graph" @default.
- W2949274727 hasPublicationYear "2011" @default.
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