New Methods for Finding Non-Left-Orderable and Unique Product Groups

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Date
2003-12-04
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Virginia Tech
Abstract

In this paper, we present techniques for proving a group to be non-left-orderable or a unique product group. These methods involve the existence of a mapping from the group to R which obeys a left-multiplication criterion. By determining the existence or non-existence of such a mapping, the desired information about the group can be concluded. As examples, we apply this technique to groups of transformations in hyperbolic 2- and 3- space, and Fibonacci groups.

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Kleinian, left-orderable, Fibonacci, unique product, Fuchsian
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