Representations of Finite Groups by Posets of Small Height

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 ≥ 8 , the cyclic group 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 ,...

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Veröffentlicht in:	Order (Dordrecht) 2024-12, Vol.41 (3), p.593-611
Hauptverfasser:	Gyenizse, Gergő, Hajnal, Péter, Zádori, László
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Sprache:	eng
Schlagworte:	Algebra Automorphisms Discrete Mathematics Group theory Lattices Mathematics Mathematics and Statistics Orbits Order Ordered Algebraic Structures
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description	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 ≥ 8 , the cyclic group 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 Z n .
doi_str_mv	10.1007/s11083-023-09649-3
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title	Representations of Finite Groups by Posets of Small Height
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