On edge-transitive metacyclic covers of cubic arc-transitive graphs of order twice a prime

Abstract

Let p be a prime, and let \(\Lambda _{2p}\) be a connected cubic arc-transitive graph of order 2p. In the literature, a lot of works have been done on the classification of edge-transitive normal covers of \(\Lambda _{2p}\) for specific \(p\le 7\). An interesting problem is to generalize these results to an arbitrary prime p. In 2014, Zhou and Feng classified edge-transitive cyclic or dihedral normal covers of \(\Lambda _{2p}\) for each prime p. In our previous work, we classified all edge-transitive N-normal covers of \(\Lambda _{2p}\), where p is a prime and N is a metacyclic 2-group. In this paper, we give a classification of edge-transitive N-normal covers of \(\Lambda _{2p}\), where \(p\ge 5\) is a prime and N is a metacyclic group of odd prime power order.