I.M.Wanless and B.S.Webb, Small partial Latin squares that cannot be embedded in a Cayley table,

and

H.Dietrich and I.M.Wanless, Small partial Latin squares that embed in an infinite group but not into any finite group.

If you want to know what format these files are in, it is my usual latin squares format.

First a catalogue of species representatives of all PLS for size up to 7

- Species of PLS of size 1
- Species of PLS of size 2
- Species of PLS of size 3
- Species of PLS of size 4
- Species of PLS of size 5
- Species of PLS of size 6
- Species of PLS of size 7

- The 300 species of PLS of size 6 that can be embedded in a cyclic group of order 6 (with the embedding given explicitly).
- The 6 species of PLS of size 6 that cannot be embedded in a cyclic group of order 6.
- The 50 smallest PLS that embed in an infinite group but not into any finite group, which answer a question of Hirsch and Jackson.