If a lattice ordered group
G
G
satisfies any identical relation, other than those satisfied by every lattice ordered group, then
G
G
is normal valued, and hence satisfies the relation
a
b
⩽
b
2
a
2
ab \leqslant {b^2}{a^2}
for all
a
,
b
⩾
e
a,b \geqslant e
.