Thirty-Third Annual Victorian Algebra Conference, Sydney, Australia, 2015

Register for: VAC33

Details of talk

TitleEmbedding partial Latin squares in Cayley tables
PresenterIan Wanless (Monash University)
Author(s)Prof Ian Wanless

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?''