It all starts with Sudoku! Indeed, when we draw up the table of a finite group, we find that every element of the group appears exactly once in each row and each column. This is because cancellation is always possible in a group. Writing \* for the operation, we have the following properties:
x \ y = x \ z implies y = z (a property concerning the rows of the group table),
and y \ x = z \ x implies y = z (a property concerning the columns of the group table).
In other words, no entry can occur more than once in any given row of the group table, and the same is true of each column.
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