\begin{definition}[Definition:Cayley Table]
A '''Cayley table''' is a technique for describing an algebraic structure (usually a finite group) by putting all the products in a square array:
:$\begin {array} {c|cccc}
\circ & a & b & c & d \\
\hline
a & a & a & b & a \\
b & b & c & a & d \\
c & d & e & f & a \\
d & c & d & a & b \\
\end {array}$
The column down the {{LHS}} denotes the first (leading) operand of the operation.
The row across the top denotes the second (following) operand of the operation.
Thus, in the above '''Cayley table''':
:$c \circ a = d$
If desired, the symbol denoting the operation itself can be put in the upper left corner, but this is not essential if there is no ambiguity.
The order in which the rows and columns are placed is immaterial.
However, it is conventional, when representing an algebraic structure with an identity element, to place that element at the head of the first row and column.
\end{definition}