- #1

fishturtle1

- 394

- 82

## Homework Statement

Compute each of the following products in ##S_9## (Write your answer as a single permutation).

a) (145)(37)(682)

## Homework Equations

Theorem: Every permutation is either the identity, a single cycle, or the product of disjoint cycles.

## The Attempt at a Solution

I start with (145)(37)(682).

Going from the rightmost cycle to the left, starting with 6.. 6 goes to 8, 8 goes to 8, then 8 goes to 8. So 6 goes to 8.

So i have (68) so far.

Now 8 goes to 2, 2 goes to 2, 2 goes to 2. So 8 goes to 2.

Now i have (682).

Now 2 goes to 6, 6 goes to 6, 6 goes to 6. So 2 goes to 6.

Now i have (6826) and I'm going to have a loop like (682682682...). I'm not sure where to go from here. If I just skip to 7, like (6827), then 2 goes to 7.. but 2 needs to go to 6 somehow. Also, by the theorem, its true that a permutation cannot be expressed as a single cycle and the product of disjoint cycles. Its a product of disjoint cycles..so is what I'm doing impossible?

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