Answer to Question #108064 in Abstract Algebra for maria

Question #108064
Find the permutation in S_4​such that 1→3, 2 2→1, 3→2.
1
Expert's answer
2020-04-06T16:39:27-0400

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

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

In our case

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



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