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Nonexistence of Idempotent Means on Free Binary Systems

  • Justin Tatch Moore (a1)
Abstract

Free binary systems are shown not to admit idempotent means. This refutes a conjecture of the author. It is also shown that the extension of Hindman’s theorem to nonassociative binary systems formulated and conjectured by the author is false.

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The research represented in this article was funded in part by NSF grant DMS–1600635.

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[1] Ellis, R., Distal transformation groups . Pacific J. Math. 8(1958), 401405. https://doi.org/10.2140/pjm.1958.8.401.
[2]S. M. Gersten and J. R. Stallings, eds. Combinatorial group theory and topology. (Papers from the conference held in Alta, Utah, July 15–18, 1984.) Annals of Mathematics Studies, 111, Princeton University Press, Princeton, NJ, 1987.
[3] Hindman, N., Finite sums from sequences within cells of a partition of N . J. Combinatorial Theory Ser. A 17(1974), 111. https://doi.org/10.1016/0097-3165(74)90023-5.
[4] Hindman, N. and Strauss, D., Algebra in the Stone-Čech compactification. de Gruyter Expositions in Mathematics, 27, Walter de Gruyter & Co., Berlin, 1998. https://doi.org/10.1515/9783110809220.
[5] Tatch Moore, J., Hindman’s theorem, Ellis’s lemma, and Thompson’s group F. In: Selected topics in combinatorial analysis, Zb. Rad. (Beograd) 17(25)(2015), 171–187.
[6] Tatch Moore, J., Nonassociative Ramsey Theory and the amenability of Thompson’s group. 2012. arxiv:1209.2063.
[7]Letter from Richard Thompson to George Francis, dated September 26, 1973.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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