Units in quasigroups with classical Bol--Moufang type identities

We proceed with Kunen's research about existence of units (left, right, two-sided) in quasigroups classical Bol--Moufang type identities, listed paper Extra loops II, by F. Fenyves (1969). consider those identities where it has not been decided yet whether a quasigroup fulfilling this identity to possess left or right identity. also provide table all Moufang--Bol indicating at each describes the variety groups, and forces out unit unit.