A Minimal Candidate for the Existence of a Weakly-Ruinous Set |
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| Authors: | John Donnelly |
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| Institution: | 1. Department of Mathematics , University of Southern Indiana , Evansville , Indiana , USA jrdonnelly@usi.edu |
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| Abstract: | We show that Richard Thompson's group F is nonamenable if and only if the three element set A 2 = {x 0 x 0 x 0, x 0 x 0 x 1, x 0 x 0 x 2} is weakly-ruinous. We then show that no two element set is weakly-ruinous, thereby showing that A 2 is minimal in both the number of elements that a weakly-ruinous set must contain and also in the number of carets that each tree in a weakly-ruinous set must have. |
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