### Abstract

We answer a question posed by Dénes and Keedwell that is equivalent to the following. For each order *n* what is the smallest size of a partial latin square that cannot be embedded into the Cayley table of any group of order *n*? We also solve some variants of this question and in each case classify the smallest examples that cannot be embedded. We close with a question about embedding of diagonal partial latin squares in Cayley tables.

Original language | English |
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Pages (from-to) | 352-363 |

Number of pages | 12 |

Journal | Australasian Journal of Combinatorics |

Volume | 67 |

Issue number | 2 |

Publication status | Published - 2017 |

## Cite this

Wanless, I., & Webb, B. S. (2017). Small partial latin squares that cannot be embedded in a Cayley table.

*Australasian Journal of Combinatorics*,*67*(2), 352-363.