Question

Show that there is not element f E S5 such that f(1,2,3)f-1 = (1,2)(3,4,5)

Show that there is not element f E S5 such that f(1,2,3)f-1 = (1,2)(3,4,5)

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Answer #1

Let

Raising both sides to power 3 we get

Which is

Which equals

But (identity) and

So we get

Meaning which is absurd

Thus, there can't exist an element such that

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