Word (Abstract Algebra)/Examples/Symmetric Group on 3 Letters

Examples of Words in the Context of Abstract Algebra
Let $S_3$ denote the Symmetric Group on 3 Letters, whose Cayley table is given as:

Consider the subset $\set {\tuple {1 2}, \tuple {132} }$ of $S_3$.

Then some of the elements of the set of words of $\set {\tuple {1 2}, \tuple {132} }$ are:
 * $\tuple {123}^2, \tuple {123}^{-1} \tuple {1 2}^2, \tuple {123} \tuple {1 2} \tuple {123}^{-1} \tuple {1 2}^{-1}, \ldots$