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: (formula). By computer enumeration we find that there are only two species of universally noncommutative loops of order = 11. Both have order 8.
|Journal||Bulletin of the Institute of Combinatorics and its Applications|
|Publication status||Published - 2011|