Automorphism group and dimension of ordered sets |
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Authors: | Gerhard Behrendt |
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Institution: | (1) Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen 1, Germany |
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Abstract: | It is shown that a finite groupG is isomorphic to the automorphism group of a two-dimensional ordered set if and only if it is a generalized wreath product of symmetric groups over an ordered index set that is a dual tree. Furthermore, every finite abelian group is isomorphic to the full automorphism group of a three-dimensional ordered set. Also every finite group is isomorphic to the automorphism group of an ordered set that does not contain an induced crown with more than four elements. |
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Keywords: | 06A06 |
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