Abelian or metacyclic covering transformation groups

Classify the arc-transitive regular covers of edge-primitive cubic graphs whose covering transformation groups are abelian or metacyclic.

Background

The paper classifies, up to isomorphism of covering graphs, connected arc-transitive regular covers of cubic edge-primitive graphs when the covering transformation group is cyclic or elementary abelian of order p^2. The remaining broader classes of abelian and metacyclic covering transformation groups are not addressed by the two classification theorems.

The authors explicitly present the classification for these larger classes as a problem following the established cyclic and elementary-abelian cases.