Find the elements Find the elements Find the elements of p₁H of μ₂H of Hp:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Consider the Cayley table below for the symmetric group S3.
![Consider the Cayley table below for the symmetric group S3.
Let H be the subgroup (μ₁) = {Po, ₁} of S3.
Po
PI P₂
μ1 1₂
flz
Po PI
P₂
142 13
PI P₂ Po flz
f42
P₂
Po PI 1₂ f3f1
12 13
Po P₁ P₂
142
μi
P₂ PO PI
H3 H3
th₂
P1 P₂
Po
Find the elements of p₁H
•
Find the elements of μ₂H
•
Find the elements of Hp₂
•
Find the elements of Huz
•
Find the distinct left cosets of H in S₂
Find the distinct right cosets of H in S₂
• What is [S₂: H]
•
Po
P1
६'
F
Pr
μi
122 flz
fes
5
441
5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03720c8a-1ad4-447f-86fd-1dd040d9c9f9%2F81c4b761-7b91-4394-bd04-83e9d3ea0b22%2Fvan6dl_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the Cayley table below for the symmetric group S3.
Let H be the subgroup (μ₁) = {Po, ₁} of S3.
Po
PI P₂
μ1 1₂
flz
Po PI
P₂
142 13
PI P₂ Po flz
f42
P₂
Po PI 1₂ f3f1
12 13
Po P₁ P₂
142
μi
P₂ PO PI
H3 H3
th₂
P1 P₂
Po
Find the elements of p₁H
•
Find the elements of μ₂H
•
Find the elements of Hp₂
•
Find the elements of Huz
•
Find the distinct left cosets of H in S₂
Find the distinct right cosets of H in S₂
• What is [S₂: H]
•
Po
P1
६'
F
Pr
μi
122 flz
fes
5
441
5.
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