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:

$\ds e$

$:=$

$\ds \text { the identity mapping}$

$\ds t$

$:=$

$\ds \tuple {1 2} \tuple {3 4}$

$\ds u$

$:=$

$\ds \tuple {1 3} \tuple {2 4}$

$\ds v$

$:=$

$\ds \tuple {1 4} \tuple {2 3}$

$\ds a$

$:=$

$\ds \tuple {1 2 3}$

$\ds b$

$:=$

$\ds \tuple {1 3 4}$

$\ds c$

$:=$

$\ds \tuple {2 4 3}$

$\ds d$

$:=$

$\ds \tuple {1 4 2}$

$\ds p$

$:=$

$\ds \tuple {1 3 2}$

$\ds q$

$:=$

$\ds \tuple {2 3 4}$

$\ds r$

$:=$

$\ds \tuple {1 2 4}$

$\ds s$

$:=$

$\ds \tuple {1 4 3}$

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