Normality of 2-Cayley digraphs

作者：Arezoomand Majid; Taeri Bijan^*

来源：Discrete Mathematics, 2015, 338(3): 41-47.

DOI：10.1016/j.disc.2014.10.019

• 2-Cayley digraph
• Normal 2-Cayley digraph
• Automorphism group of digraph

A digraph Gamma is called a 2-Cayley digraph over a group G, if there exists a semiregular subgroup R-G of Aut(Gamma) isomorphic to G with two orbits. We say that Gamma is normal if RG is a normal subgroup of Aut(Gamma). In this paper, we determine the normalizer of RG in Aut(Gamma). We show that the automorphism group of each normal 2-Cayley digraph over a group with solvable automorphism group, is solvable. We prove that for each finite group G not equal Q(8) x Z(2)(r), r >= 0, where Q(8) is the quaternion group of order 8 and Z(2) is the cyclic group of order 2, there exists a normal 2-Cayley graph over G and that every finite group has a normal 2-Cayley digraph.

• 出版日期2015-3-6