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Let f(1 2 3) E S3. Find the maps in the following sequence131.f.f2,3,f4f5..Do you see apattern?

Question
Let f
(1 2 3) E S3. Find the maps in the following sequence
131.f.f2,3,f4f5..
Do you see a
pattern?
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Let f (1 2 3) E S3. Find the maps in the following sequence 131.f.f2,3,f4f5.. Do you see a pattern?

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check_circleAnswer
Step 1

We are given that f = (1 2 3) ∊ S3.

The identity of S3 is written as 1[3] = e = (1) (2) (3) .

Now, we need to find f, f2, f3, f4, f5, …

Step 2

Now,

...
f2 (1 2 3) (1 2 3)
1 2 3
2
3
2 3
2 3
1
2 3
1
3 1
2
= (13 2)
f3
f2f= (13 2)(1 2 3)
1 2 3'
1
3
2
3 1
2
3
2
1 2
3
= e
ft f3 f ef= f = (12 3)
f5= ff=ff- f2 = (13 2)
23
l
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f2 (1 2 3) (1 2 3) 1 2 3 2 3 2 3 2 3 1 2 3 1 3 1 2 = (13 2) f3 f2f= (13 2)(1 2 3) 1 2 3' 1 3 2 3 1 2 3 2 1 2 3 = e ft f3 f ef= f = (12 3) f5= ff=ff- f2 = (13 2) 23 l

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