二面体群D_(2p)的出度为3的Cayley有向图的正规性

The Normality of Cayley Digraphs of Out valency 3 of Dihedral Groups of Order Twice a Prime

设Ｇ是一个有限群，Ｘ＝Ｃａｙ（Ｇ，Ｓ）是Ｇ关于Ｓ的Ｃａｙｌｅｙ有向图，称Ｘ关於群Ｇ是正规的，如果Ｇ的右正则表示Ｒ（Ｇ）在Ｘ的自同构群Ａｕｔ（Ｘ）中是正规的．设Ｄ２ｐ是２ｐ阶二面体群（ｐ为素数），本文考察了Ｃａｙ（Ｄ２ｐ，Ｓ）（其中｜Ｓ｜＝３）关於Ｄ２ｐ的正规性，并给出了这些图的全自同构群．

e call a Cayley digraph X=Cay(G,S) normal for G if the right regular representation R(G) of G is normal in the automorphism group Aut(X) of X.In this paper we study the normality of Cayley digraph of out valency 3 of dihedral groups of order twice a prime and we also determine the automerphism groups of these digraphs.