三类2q^2p阶群的3度Cayley图

Cubic Cayley Graphs on Three Kinds of Groups with Order 2q^2p

称有限群G的Cayley图Γ是正规Cayley图,如果G的右正则表示R(G)正规于图Γ的全自同构群Aut(Γ)。研究了三类2q2p阶亚循环群的连通3度Cayley图的正规性,其中q<p均为奇素数,且q(p-1)。作为应用,决定了其中两类亚循环群的弱3-CI性。值得一提的是,在此用到单群分类定理。

A Cayley （di）graph Г of a finite group G is said to be normal if the action of G on V（Г） by right multiplieation is normal in the full automor-phism group of Г. This paper mainly researehes the mormality of connected cubic Cayley graphs on three kinds of metacyclic groups with order 2q2p,where both q〈p are odd primes and q ｜（p-1）. In application,the weak 3-CI property of two kinds of groups are determined. The conclusion also involves in the classification of the finite simple groups.