Abstract
We characterize the finite groups as the automorphism groups of the finite height one posets with at most four orbits. We also prove that for each \(n\ge 8\), the cyclic group \(\textbf{Z}_n\) is isomorphic to the automorphism group of a finite height one poset with at most two orbits. As a consequence, for each n, we determine the minimum size of the posets whose automorphism groups are isomorphic to \(\textbf{Z}_n\).
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Acknowledgements
We would like to thank one of the anonymous referees for their detailed comments and suggestions that led to an improved version of our manuscript.
Funding
The research of authors was partially supported by the grants NKFIH-K128042, NKFIH-K138892, and TKP2021-NVA-09 of the Ministry for Innovation and Technology, Hungary.
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Gyenizse, G., Hajnal, P. & Zádori, L. Representations of Finite Groups by Posets of Small Height. Order (2023). https://doi.org/10.1007/s11083-023-09649-3
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DOI: https://doi.org/10.1007/s11083-023-09649-3