Answer to Question #108064 in Abstract Algebra for maria

Question

Find the permutation in S_4​such that 1→3, 2 2→1, 3→2.

Answer 1

$S_4$ the symmetric group of all permutations of 4 elements.

It has 4!=24 elements. For example, $\begin{pmatrix} 1 & 2&3&4 \\ 1&2&3&4 \end{pmatrix}, \begin{pmatrix} 1 & 2&3&4 \\ 2&1&4&3 \end{pmatrix}=(1,2)(3,4)$ .

In our case

$\begin{pmatrix} 1 & 2&3&4 \\ 3&1&2&4 \end{pmatrix}=(1,3,2)(4) or (1,3,2)$