A graph Γ is said to be G-locally primitive, whereG is a subgroup of automorphisms of Γ, if the stabiliser Gα of a vertex α acts primitively on the set Γ(α) of vertices of Γ adjacent to α. For a finite non-abe...A graph Γ is said to be G-locally primitive, whereG is a subgroup of automorphisms of Γ, if the stabiliser Gα of a vertex α acts primitively on the set Γ(α) of vertices of Γ adjacent to α. For a finite non-abelian simple group L and a Cayley subset S of L, suppose that LG≤Aut(L), and the Cayley graph Γ=Cay (L, S) is G-locally primitive. In this paper we prove that L is a simple group of Lie type, and either the valency of Γ is an add prine divisor of ｜Out(L)｜, or L=PΩ+8 (q) and Γ has valency 4. In either cases, it is proved that the full automorphism group of Γ is also almost simple with the same socle L.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 69873002).
文摘A graph Γ is said to be G-locally primitive, whereG is a subgroup of automorphisms of Γ, if the stabiliser Gα of a vertex α acts primitively on the set Γ(α) of vertices of Γ adjacent to α. For a finite non-abelian simple group L and a Cayley subset S of L, suppose that LG≤Aut(L), and the Cayley graph Γ=Cay (L, S) is G-locally primitive. In this paper we prove that L is a simple group of Lie type, and either the valency of Γ is an add prine divisor of ｜Out(L)｜, or L=PΩ+8 (q) and Γ has valency 4. In either cases, it is proved that the full automorphism group of Γ is also almost simple with the same socle L.
