Answer to Question #107869 in Abstract Algebra for maria

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

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

It has 4!=24 elements. For example, 

"\\begin{pmatrix} 1 & 2&3&4 \\\\ \n1&2&3&4 \\end{pmatrix}, \n\\begin{pmatrix} 1 & 2&3&4 \\\\ \n4&3&2&1 \\end{pmatrix}=(1,4)(2,3)\\\\\nor \\\\\n1\\to4, 2\\to3,3\\to2,4\\to1"

In our case

"1\\to3, 2\\to1, 3\\to2\\\\\n\\begin{pmatrix} 1 & 2&3&4 \\\\ \n3&1&2&4 \\end{pmatrix}=(1,3,2)(4) =(1,3,2)"


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