### Abstract

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: (., alpha, beta; alpha, ., gamma;
beta, gamma, .) (fig.1) By computer enumeration we find that
there are only two species of universally non commutative
loops of order =<11. Both have order 8

Original language | English |
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Pages (from-to) | 113 - 115 |

Number of pages | 3 |

Journal | Bulletin of the Institute of Combinatorics and its Applications |

Volume | 61 |

Publication status | Published - 2011 |

## Cite this

Brouwer, A., & Wanless, I. M. (2011). Universally noncommutative loops.

*Bulletin of the Institute of Combinatorics and its Applications*,*61*, 113 - 115.