Trees and the bireflection property |
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Authors: | Gadi Moran |
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Institution: | (1) Department of Mathematics, University of Haifa, Haifa, Israel |
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Abstract: | The group of automorphisms of a tree (partially ordered set where the set of predecessors of an element is well ordered) with
no infinite levels enjoys the property that every member is a product of two elements of order ≦2. It is shown that this property—called
the bireflection property—fails for some trees having infinite levels. In fact, every subtree of a treeT has the the bireflection property if and only if the tree of all zero-one sequences of length ≦ω with finitely many ones
is not embeddable inT. |
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Keywords: | |
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