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2Let o (1 3 5)(2 4) and T (1 5)(2 3) be elements of S. Find o,or,to, and to

Question
2
Let o (1 3 5)(2 4) and T (1 5)(2 3) be elements of S. Find o,or,to, and to
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2 Let o (1 3 5)(2 4) and T (1 5)(2 3) be elements of S. Find o,or,to, and to

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check_circleAnswer
Step 1

Note: Here the operation is composition of permutation group S3.

(135) (2 4) and
τ- (15 ) (23 ) are the
We are given that σ
elements of S3.
Weneed to find (a ) σ?, (b) στ, (c) το and (d) τσ .
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(135) (2 4) and τ- (15 ) (23 ) are the We are given that σ elements of S3. Weneed to find (a ) σ?, (b) στ, (c) το and (d) τσ .

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Step 2

Rewriting the elements,

5
4 5
(2 4
1
3
1
2
3
(13 5) (2 4)
a
4 5
5
3
4
2
2
4 5
5
1
2
(15) (2 3)
and τ=
5
3
2
3
2
4
1
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5 4 5 (2 4 1 3 1 2 3 (13 5) (2 4) a 4 5 5 3 4 2 2 4 5 5 1 2 (15) (2 3) and τ= 5 3 2 3 2 4 1

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Step 3

Now,

...
4 5
4 5
5
3
1
2
3
(1
2
3
1
2
3
4
(a) a2
4 5
5
5
3
3
4
2
1
4
2
2
(1 5
3)
4 5
1
(b) στ:
2
3
1
2
3
1
2
3
4
5)
5
5 3
5
3
4
2
1
4
2
2
4
3 4)
(2 5
45
5
2
3
(1
2
3
2
3
4
( c) τσ
4 5
5
3
2
3
2
4
1
3
4
2
(1 2
4 3)
2 3
45
5)
1
2
4
(
1
2
3
1
4
( d) τσ2
4
5
2
4
3
4 5
5
3
2
1
2
3
1
3
4
2
5
4 5
3
2
.5
5 3
2
1
2
1
4
3
4
4
G
3
4
2
(2 3 5)
LO CO
LO
LO LO
Ln N
L H
23 51o
Il
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4 5 4 5 5 3 1 2 3 (1 2 3 1 2 3 4 (a) a2 4 5 5 5 3 3 4 2 1 4 2 2 (1 5 3) 4 5 1 (b) στ: 2 3 1 2 3 1 2 3 4 5) 5 5 3 5 3 4 2 1 4 2 2 4 3 4) (2 5 45 5 2 3 (1 2 3 2 3 4 ( c) τσ 4 5 5 3 2 3 2 4 1 3 4 2 (1 2 4 3) 2 3 45 5) 1 2 4 ( 1 2 3 1 4 ( d) τσ2 4 5 2 4 3 4 5 5 3 2 1 2 3 1 3 4 2 5 4 5 3 2 .5 5 3 2 1 2 1 4 3 4 4 G 3 4 2 (2 3 5) LO CO LO LO LO Ln N L H 23 51o Il

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