Lifting a prescribed group of automorphisms of graphs

Potočnik, Primož; Spiga, Pablo

doi:10.1090/proc/14609

Lifting a prescribed group of automorphisms of graphs
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by Primož Potočnik and Pablo Spiga PDF

Proc. Amer. Math. Soc. 147 (2019), 3787-3796 Request permission

Abstract:

In this paper we are interested in lifting a prescribed group of automorphisms of a finite graph via regular covering projections. Let $\Gamma$ be a finite graph and let $\mathrm {Aut}(\Gamma )$ be the automorphism group of $\Gamma$. It is well known that we can always find a finite graph $\tilde {\Gamma }$ and a regular covering projection $\wp \colon \tilde {\Gamma } \to \Gamma$ such that $\mathrm {Aut}(\Gamma )$ lifts along $\wp$. However, for constructing peculiar examples and in applications it is often important, given a subgroup $G$ of $\mathrm {Aut}(\Gamma )$, to find $\wp$ along which $G$ lifts but no further automorphism of $\Gamma$ does, or even that $\mathrm {Aut}(\tilde {\Gamma })$ is the lift of $G$. In this paper, we address these problems.

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