Cyclic Permutation/Examples/Symmetric Group on 3 Letters

Examples of Cyclic Permutations

Each of the non-identity elements of the Symmetric Group on 3 Letters is a cyclic permutation.

Expressed in cycle notation, they are as follows:

\(\ds e\)

\(:=\)

\(\ds \text { the identity mapping}\)

\(\ds p\)

\(:=\)

\(\ds \tuple {1 2 3}\)

\(\ds q\)

\(:=\)

\(\ds \tuple {1 3 2}\)

\(\ds r\)

\(:=\)

\(\ds \tuple {2 3}\)

\(\ds s\)

\(:=\)

\(\ds \tuple {1 3}\)

\(\ds t\)

\(:=\)

\(\ds \tuple {1 2}\)

Sources

• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $9$: Permutations: Example $9.3$