Symmetric Group on 3 Letters/Cycle Notation

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Cycle Notation for Symmetric Group on $3$ Letters

The symmetric group on $3$ letters can be given in cycle notation as follows:

\(\displaystyle e\) \(:=\) \(\displaystyle \text { the identity mapping}\)
\(\displaystyle p\) \(:=\) \(\displaystyle \tuple {1 2 3}\)
\(\displaystyle q\) \(:=\) \(\displaystyle \tuple {1 3 2}\)


\(\displaystyle r\) \(:=\) \(\displaystyle \tuple {2 3}\)
\(\displaystyle s\) \(:=\) \(\displaystyle \tuple {1 3}\)
\(\displaystyle t\) \(:=\) \(\displaystyle \tuple {1 2}\)