# Small Partial Latin Squares that Cannot be Embedded in a Cayley Table

We answer a question posed by Déenes 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.