On the Stabilizer of the Automorphism Group of a 4—valent Vertex—transitive Graph with Odd—prime—power Order

Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p^κ（κ≥1） and let A be the full automorphism group of X.In this paper,we prove that the stabilizer Av of a vertex v in A is a 2-group if p≠5,or a {2,3}-group if p=5.Furthermore,if p=5|Av| is not divisible by 3^2.As a result ,we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p^κ(κ≥1） is at most 1-arc-transitive for p≠5 and 2-arc-transitive for p=5.     

n-Lie代数的Frattini子代数及非嵌入定理

In this paper,we prove the nonimbedding theorem in nilpotent n-Liealgebras which is an analogue to the nonimbedding theorem of Burnsids in groupsof prime power order.We also study the properties of Frattini subalgebras of n-Liealgebras over the field with characteristic zero,and prove that the Frattini subalgebraof any k-solvable(k≥2)n-Lie algebra is zero.