Geodesic
On Two Problems Related to Associators of Moufang Loops
Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 211-214 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Moufang loop $M$ of order $3^{19}$ is constructed, together with a pair $a$, $b$ of elements of $M$, such that the set of all elements of $M$ associating with $a$ and $b$ is not a subloop. This also gives an example of a nonassociative Moufang loop with a generating set in which every three elements have trivial associator.
Keywords: Moufang loop
Mots-clés : associator, subloop. 
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I. B. Gorshkov; A. N. Grishkov; A. V. Zavarnitsine. On Two Problems Related to Associators of Moufang Loops. Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 211-214. http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a5/

[1] H. O. Pflugfelder, Quasigroups and Loops: Introduction., Sigma Ser. in Pure Math., 7, Heldermann Verlag, Berlin, 1990 | MR | Zbl

[2] V. D. Belousov, Osnovy teorii kvazigrupp i lup, Nauka, M., 1967 | MR | Zbl

[3] A. Drápal, “A simplified proof of Moufang's theorem”, Proc. Amer. Math. Soc., 139:1 (2011), 93–98 | DOI | MR | Zbl

[4] E. N. Kuzmin, “O svyazi mezhdu algebrami Maltseva i analiticheskimi lupami Mufang”, Algebra i logika, 10 (1971), 3–22 | MR | Zbl

[5] A. A. Sagle, “Malcev algebras”, Trans. Amer. Math. Soc., 101 (1961), 426–458 | DOI | MR | Zbl