Abstract

Sudoku puzzles are examples of a combinatorial object called a partial Latin square (PLS). In 1974 Denes and Keedwell asked for each n what is the smallest PLS that cannot embed into any group table of order n. In 2012 Hirsch and Jackson asked what is the smallest PLS that can be embedded in an infinite group but not into any finite group. We answer both these questions and a couple of related ones.



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