Abstract: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.
Keywords: quasigroup; Bol--Moufang type identity; right unit; left unit
DOI: DOI 10.14712/1213-7243.2020.039
AMS Subject Classification: 20N05