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:
| \(\ds e\) | \(:=\) | \(\ds \text { the identity mapping}\) | ||||||||||||
| \(\ds p\) | \(:=\) | \(\ds \tuple {1 2 3}\) | ||||||||||||
| \(\ds q\) | \(:=\) | \(\ds \tuple {1 3 2}\) |
| \(\ds r\) | \(:=\) | \(\ds \tuple {2 3}\) | ||||||||||||
| \(\ds s\) | \(:=\) | \(\ds \tuple {1 3}\) | ||||||||||||
| \(\ds t\) | \(:=\) | \(\ds \tuple {1 2}\) |