Hindman's Theorem, Ellis's Lemma, and Thompson's group $F$

Abstract

The purpose of this article is to formulate conjectural generalizations of Hindman's Theorem and Ellis's Lemma for nonassociative binary systems and relate them to the amenability problem for Thompson's group $F$. Partial results are obtained for both conjectures. The paper will also contain some general analysis of the conjectures.

arXiv commentThis paper has now appeared but is largely obsolete: Conjectures 1.3 and 1.4 have since been refuted by the author. arXiv admin note: text overlap with arXiv:1209.2063