Answer to Question #107869 in Abstract Algebra for maria

Question

Find the permutation in S_4
​
such that 1→3, 2 12→1, 23→2.

Answer 1

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

It has 4!=24 elements. For example, 

$\begin{pmatrix} 1 & 2&3&4 \\ 1&2&3&4 \end{pmatrix}, \begin{pmatrix} 1 & 2&3&4 \\ 4&3&2&1 \end{pmatrix}=(1,4)(2,3)\\ or \\ 1\to4, 2\to3,3\to2,4\to1$

In our case

$1\to3, 2\to1, 3\to2\\ \begin{pmatrix} 1 & 2&3&4 \\ 3&1&2&4 \end{pmatrix}=(1,3,2)(4) =(1,3,2)$