Lifting a prescribed group of automorphisms of graphs
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- by Primož Potočnik and Pablo Spiga
- Proc. Amer. Math. Soc. 147 (2019), 3787-3796
- DOI: https://doi.org/10.1090/proc/14609
- Published electronically: May 1, 2019
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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.References
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Bibliographic Information
- Primož Potočnik
- Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
- Email: primoz.potocnik@fmf.uni-lj.si
- Pablo Spiga
- Affiliation: Dipartimento di Matematica Pura e Applicata, University of Milano-Bicocca, Via Cozzi 55, 20126 Milano Italy
- MR Author ID: 764459
- Email: pablo.spiga@unimib.it
- Received by editor(s): January 7, 2018
- Received by editor(s) in revised form: January 8, 2019, and January 16, 2019
- Published electronically: May 1, 2019
- Additional Notes: The first author gratefully acknowledges financial support of the Slovenian Research Agency, ARRS, research program no. P1-0294.
- Communicated by: Pham Huu Tiep
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3787-3796
- MSC (2010): Primary 20B25, 05C20, 05C25
- DOI: https://doi.org/10.1090/proc/14609
- MathSciNet review: 3993771