Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-25T05:59:48.086Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonexistence of Idempotent Means on Free Binary Systems

Part of: Graph theory Abstract harmonic analysis

Published online by Cambridge University Press:  11 January 2019

Justin Tatch Moore
Justin Tatch Moore*
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853-4201, USA Email: justin@math.cornell.edu
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

amenabilitybinary systemEllis’s Lemmaidempotent meanHindman’s TheoremmagmanonassociativeThompson’s group

MSC classification

Primary: 43A07: Means on groups, semigroups, etc.; amenable groups
Secondary: 05C55: Generalized Ramsey theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 3 , September 2019 , pp. 577 - 581
Copyright
© Canadian Mathematical Society 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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

References

Ellis, R., Distal transformation groups . Pacific J. Math. 8(1958), 401–405. https://doi.org/10.2140/pjm.1958.8.401.Google Scholar
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.Google Scholar
Hindman, N., Finite sums from sequences within cells of a partition of N . J. Combinatorial Theory Ser. A 17(1974), 1–11. https://doi.org/10.1016/0097-3165(74)90023-5.Google Scholar
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.Google Scholar
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.Google Scholar
Tatch Moore, J., Nonassociative Ramsey Theory and the amenability of Thompson’s group. 2012. arxiv:1209.2063.Google Scholar
Letter from Richard Thompson to George Francis, dated September 26, 1973.Google Scholar