Basarab A.S.
Osborn's G-loops
It is proved, that if in a loop Q(·) the equality
(·)I-1x= Ix(·) holds for every x
ÎQ, then
Q(·) is a G-loop.
From this result it follows that:
a) An Osborn's loop Q(·) in which x2 Î N for every xÎ Q is a G-loop;
b) every i-loop is a G-loop.