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Graphs with Subconstituents Containing L 3 (p)

1982
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Proceedings of the American Mathematical Society
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Let T be a finite connected undirected graph, G a vertex-transitive subgroup of aut(T), {x, y) an edge of T and G,(x, y) the subgroup of G fixing every vertex at a distance of at most i from x or y. We show that if the stabilizer Gx contains a normal subgroup inducing L}(p), p a prime, on the set of vertices adjacent to x, then G5(x, y) = 1. Let T be an undirected graph with vertex set V(T) and edge set E(T) and let G be a subgroup of aut(T).

doi:10.2307/2044088
fatcat:j5msyxlf55bytkr3qb2rsdmqs4