Write down the six elements of S3 and give the multiplication table for the group. The six elements of S3 are then: 1 2 1 3 1 = (1 ²23). a = (²2 ²3). b = (²²2) 1 3 1 1 c = (2²²3). α = (²2²3). == (1 3²2) 1 The multiplication table for S3 can be written down directly by doing the required composition. Find ab, de,and c^2 2 3 2 3 2 3 2 3 a = ( ²2 ²3 ³) a = ( ²2 ²3 ³)=b (² ² 2) ² = ( 2² ²³) a= 1 1 3 1 a3 = (₁ 2²3) = 1 1 2 2 2 c = ( ₂2 ²3 ) c = ( ₂2 ² 3) = c ² = c = (₁ ²₂3) ²¹ C 1 1 2
Write down the six elements of S3 and give the multiplication table for the group. The six elements of S3 are then: 1 2 1 3 1 = (1 ²23). a = (²2 ²3). b = (²²2) 1 3 1 1 c = (2²²3). α = (²2²3). == (1 3²2) 1 The multiplication table for S3 can be written down directly by doing the required composition. Find ab, de,and c^2 2 3 2 3 2 3 2 3 a = ( ²2 ²3 ³) a = ( ²2 ²3 ³)=b (² ² 2) ² = ( 2² ²³) a= 1 1 3 1 a3 = (₁ 2²3) = 1 1 2 2 2 c = ( ₂2 ²3 ) c = ( ₂2 ² 3) = c ² = c = (₁ ²₂3) ²¹ C 1 1 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Write down the six elements of S3 and give the multiplication table for
the group.
The six elements of S3 are then:
2
2
2
3
1 = (1/²/3)
a =
(2²2 ² 3).
b =
(² ² 2)
2
3 1
3 1
1
1
2
c = (²2²3). d= (² 2 3). e= (1 ² 3)
C
1
3 1
3
The multiplication table for S3 can be written down directly by doing
the required composition. Find ab, de,and c^2
1 2
1 2
1 2
2 3
a = (2²2 ²7 ³3)
a = ( 2² ²3 ³ ) = b (² ² 2) ²= ( 2₂ ²3 ³)
a=
3
1
1
3 1
1.
= (1 2² ₂3 )
= 1
2
1
2
2
1
c = ( ²2 ²3 ) c = ( 2₂ ²3 ) = c ² = c = (₁ ²²3) ²¹
C
C
1
1
2 3.
a3 =
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