Geodesic
Units in quasigroups with classical Bol--Moufang type identities
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 4, pp. 427-435.

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We proceed with Kunen's research about existence of units (left, right, two-sided) in quasigroups with classical Bol--Moufang type identities, listed in paper Extra loops II, by F. Fenyves (1969). We consider those Bol--Moufang identities where it has not been decided yet whether a quasigroup fulfilling this identity has to possess a left or right identity. We also provide a table of all Moufang--Bol identities, indicating at each whether it describes the variety of groups, and whether it forces out the left unit or the right unit.
DOI : 10.14712/1213-7243.2020.039
Classification : 20N05
Keywords: quasigroup; Bol--Moufang type identity; right unit; left unit 
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Didurik, Natalia; Shcherbacov, Victor. Units in quasigroups with classical  Bol--Moufang type identities. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 4, pp. 427-435. doi : 10.14712/1213-7243.2020.039. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.039/

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