Lifts of Automorphisms of Symmetric Digraphs Associated With Cyclic Abelian Covers III

Abstract

Let $D$ be a connected symmetric digraph, $\mathrm{\Gamma }$ a group of automorphisms of $D$, and $A$ a finite abelian group. For a cyclic $A$-cover of $D$, we consider a lift of $\gamma \in \mathrm{\Gamma }$, and the associated group automorphism of some subgroup of $AutA$. Furthermore, we give a characterization for any $\gamma \in \mathrm{\Gamma }$ to have a lift in terms of some matrix.