Diagram groups are totally orderable |
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Authors: | VS Guba MV Sapir |
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Institution: | a Department of Mathematics, Vologda State University, Russia b Department of Mathematics, Vanderbilt University, USA |
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Abstract: | In this paper, we introduce the concept of the independence graph of a directed 2-complex. We show that the class of diagram groups is closed under graph products over independence graphs of rooted 2-trees. This allows us to show that a diagram group containing all countable diagram groups is a semi-direct product of a partially commutative group and R. Thompson's group F. As a result, we prove that all diagram groups are totally orderable. |
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Keywords: | 20F65 |
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