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What are the possible orders for the elements of S6 and A6

Chapter 5, Problem 9E

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QUESTION:

What are the possible orders for the elements of S6 and A6? What about A7? (This exercise is referred to in Chapter 25.)

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QUESTION:

What are the possible orders for the elements of S6 and A6? What about A7? (This exercise is referred to in Chapter 25.)

ANSWER:

Step 1 of 2

To find the possible orders for the elements of , first let us focus on the possible partitions of .

Now, if we consider each partition as a product of disjoint cycles, then the length of each cycle is the least common multiple of the cycles.

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