# Universally noncommutative loops

We call a loop universally noncommutative if it does not have
a loop isotope in which two non-identity elements commute.
Finite universally noncommutative loops are equivalent to
latin squares that avoid the configuration:
.ab
a.c
bc.

By computer enumeration we find that there are only two species of
universally noncommutative loops of order ≤11. Both have
order 8.