Question #107869
Find the permutation in S_4

such that 1→3, 2 12→1, 23→2.
1
Expert's answer
2020-04-06T17:26:36-0400

S4S_4  the symmetric group of all permutations of 4 elements.

It has 4!=24 elements. For example, 

(12341234),(12344321)=(1,4)(2,3)or14,23,32,41\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

13,21,32(12343124)=(1,3,2)(4)=(1,3,2)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)


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