# Details of talk

Title | Embedding partial Latin squares in Cayley tables |
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Presenter | Ian Wanless (Monash University) |

Author(s) | Prof Ian Wanless |

Session | n/a |

Time | |

Abstract | A partial Latin square (PLS) can be thought of as a finite set of triples where no two distinct triples agree in more than one position. A group operation $\circ$ can be defined by triples of the form $(g,h,g\circ h)$. We say that a PLS embeds in a group if the set of triples which define the group contains an (appropriately relabelled) copy of the PLS. In this talk I will briefly survey some combinatorial problems related to embeddings of PLS in groups. I will then present some new results that answer questions published by Denes and Keedwell, and by Hirsch and Jackson. The most interesting of these questions turns out to be ``What is the smallest PLS that can be embedded into some infinite group but does not have an embedding into any finite group?'' |