Geodesic
Nonexistence of Idempotent Means on Free Binary Systems
Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 577-581

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2018-038-5
Mots-clés : amenability, binary system, Ellis’s Lemma, idempotent mean, Hindman’s Theorem, magma, nonassociative, Thompson’s group 
Moore, Justin Tatch. Nonexistence of Idempotent Means on Free Binary Systems. Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 577-581. doi: 10.4153/CMB-2018-038-5
@article{10_4153_CMB_2018_038_5,
     author = {Moore, Justin Tatch},
     title = {Nonexistence of {Idempotent} {Means} on {Free} {Binary} {Systems}},
     journal = {Canadian mathematical bulletin},
     pages = {577--581},
     year = {2019},
     volume = {62},
     number = {3},
     doi = {10.4153/CMB-2018-038-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-038-5/}
}
TY  - JOUR
AU  - Moore, Justin Tatch
TI  - Nonexistence of Idempotent Means on Free Binary Systems
JO  - Canadian mathematical bulletin
PY  - 2019
SP  - 577
EP  - 581
VL  - 62
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-038-5/
DO  - 10.4153/CMB-2018-038-5
ID  - 10_4153_CMB_2018_038_5
ER  - 
%0 Journal Article
%A Moore, Justin Tatch
%T Nonexistence of Idempotent Means on Free Binary Systems
%J Canadian mathematical bulletin
%D 2019
%P 577-581
%V 62
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-038-5/
%R 10.4153/CMB-2018-038-5
%F 10_4153_CMB_2018_038_5

[1] Ellis, R., Distal transformation groups . Pacific J. Math. 8(1958), 401–405. . Google Scholar | DOI

[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. Google Scholar

[3] Hindman, N., Finite sums from sequences within cells of a partition of N . J. Combinatorial Theory Ser. A 17(1974), 1–11. . Google Scholar | DOI

[4] Hindman, N. and Strauss, D., Algebra in the Stone-Čech compactification. de Gruyter Expositions in Mathematics, 27, Walter de Gruyter & Co., Berlin, 1998. . Google Scholar | DOI

[5] Tatch Moore, J., Hindman’s theorem, Ellis’s lemma, and Thompson’s group F. In: Selected topics in combinatorial analysis, Zb. Rad. (Beograd) (25)(2015), 171–187. Google Scholar

[6] Tatch Moore, J., Nonassociative Ramsey Theory and the amenability of Thompson’s group. 2012. arxiv:1209.2063. Google Scholar

[7] Letter from Richard Thompson to George Francis, dated September 26, 1973. Google Scholar

Cité par Sources :