# Notes - Groups HT23, Cayley tables

### Flashcards

What is in the $(i, j)$-th entry of the Cayley table for $G$?

\[g_i \ast g_j\]

What mneumonic helps you remember the order in which to look up a product in a Cayley table?

Down the corridor, along the stairs.

### Proofs

Prove that every Cayley table has the Latin square property, i.e. that every element of $G$ appears one in each row and each column.

Todo.