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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
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Abstract

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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 

Footnotes

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

References

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