| Speaker: Jiali Du Affiliation: Beijing Jiaotong University Time: 13:00 Wednesday, 2 May, 2018 Location: 303-257 |
| Let Gamma be a graph and let G be a group of automorphisms of Gamma. The graph Gamma is called G-normal if G is normal in the automorphism group of Gamma. Let T be a finite non-abelian simple group and let G = T^k with k>0. In this talk, I will give a proof that: if every connected pentavalent symmetric T-vertex-transitive graph is T-normal, then every connected pentavalent symmetric G-vertex-transitive graph is G-normal. This result, among others, implies that every connected pentavalent symmetric G-vertex-transitive graph is G-normal except if T is one of 57 simple groups. Furthermore, every connected pentavalent symmetric G-regular graph is G-normal except if T is one of 20 simple groups, and every connected pentavalent G-symmetric graph is G-normal except if T is one of 17 simple groups. |