Let $\sigma$ be the permutation given by 
Is their a short way to do this.Thanks
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Matt Samuel
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Sophie Clad
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Write $\sigma$ as a product of disjoint cycles. – Dec 31 '15 at 07:42
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I guess this was downvoted because it's a pasted image with multiple choice answers. I don't see a problem with the question. – Matt Samuel Dec 31 '15 at 07:43
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We have a cycle of length 4, a cycle of length 3, and a cycle of length 2. Raising to a power that is a multiple of 4 makes the length 4 cycle go away, as well as the length 2. Raising to a multiple of 3 makes the 3-cycle go away. But we want them all to go away. What can we do?
Matt Samuel
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"Raising to a power that is a multiple of 4 makes the length 4 cycle go away"..Why is that so? – Sophie Clad Dec 31 '15 at 07:54
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@Sophie try explicitly raising a 4 cycle to the fourth power and you'll see. In general an $n$-cycle has order $n$. The reason the method in the other answer works is because the disjoint cycles commute, so raising the permutation to a power is the same as raising all of the cycles to the same power. – Matt Samuel Dec 31 '15 at 07:57
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Hint: Every permutation can be written as a product of disjoint cycles. The order of the permutation is the least common multiple of the order of each cycle.
AnotherPerson
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