A graph Г is said to be G-locally primitive, where G is a subgroup of automorphisms of Г, if the stabiliser Ga of a vertex α acts primitively on the set Г( α ) of vertices of Г adjacent to α. For a finite non-a...A graph Г is said to be G-locally primitive, where G is a subgroup of automorphisms of Г, if the stabiliser Ga of a vertex α acts primitively on the set Г( α ) of vertices of Г adjacent to α. For a finite non-abelian simple group L and a Cayley subset S of L, suppose that L ? G ? Aut( L), and the Cayley graph Г = 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 Г is an add prine divisor of |Out(L)|, orL =PΩ 8 + (q) and Г has valency 4. In either cases, it is proved that the full automorphism group of Г 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 Г is said to be G-locally primitive, where G is a subgroup of automorphisms of Г, if the stabiliser Ga of a vertex α acts primitively on the set Г( α ) of vertices of Г adjacent to α. For a finite non-abelian simple group L and a Cayley subset S of L, suppose that L ? G ? Aut( L), and the Cayley graph Г = 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 Г is an add prine divisor of |Out(L)|, orL =PΩ 8 + (q) and Г has valency 4. In either cases, it is proved that the full automorphism group of Г is also almost simple with the same socle L.
