Alternating Group on 4 Letters/Cycle Notation

Cycle Notation for Alternating Group on $4$ Letters

The alternating group on $4$ letters can be given in cycle notation as follows:

\(\ds e\)

\(:=\)

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

\(\ds t\)

\(:=\)

\(\ds \tuple {1 2} \tuple {3 4}\)

\(\ds u\)

\(:=\)

\(\ds \tuple {1 3} \tuple {2 4}\)

\(\ds v\)

\(:=\)

\(\ds \tuple {1 4} \tuple {2 3}\)

\(\ds a\)

\(:=\)

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

\(\ds b\)

\(:=\)

\(\ds \tuple {1 3 4}\)

\(\ds c\)

\(:=\)

\(\ds \tuple {2 4 3}\)

\(\ds d\)

\(:=\)

\(\ds \tuple {1 4 2}\)

\(\ds p\)

\(:=\)

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

\(\ds q\)

\(:=\)

\(\ds \tuple {2 3 4}\)

\(\ds r\)

\(:=\)

\(\ds \tuple {1 2 4}\)

\(\ds s\)

\(:=\)

\(\ds \tuple {1 4 3}\)

Sources

• 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $9$: Permutations: Exercise $3$