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Let n be a positive integer. If n is odd, is an n-cycle an

Chapter 5, Problem 15E

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QUESTION:

Problem 15E

Let n be a positive integer. If n is odd, is an n-cycle an odd or an even permutation? If n is even, is an n-cycle an odd or an even permutation?

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QUESTION:

Problem 15E

Let n be a positive integer. If n is odd, is an n-cycle an odd or an even permutation? If n is even, is an n-cycle an odd or an even permutation?

ANSWER:

Step 1 of 2

For a given positive integer , permutation is a product such that it has  cycles.

Thus, for positive odd integer , will always be even.

Hence,  if  is odd, the n-cycle will be an even permutation.

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