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Question 2. Consider the following function f: D3 → S3, Where D3 = {Ro, R120, R240, L, R120L, R240L} is the dihedral group of order 6 and S3 = {(1), (12), (13), (23), (123), (132)} is the symmetric group of order 6 f(x) Ro, (1) R120 (12) R240 (13) Explain why f is not a homomorphism L (23) R120L R240L (123) (132)

Question 2. Consider the following function f: D3 → S3, Where D3 = {Ro, R120, R240, L, R120L, R240L} is the dihedral group of order 6 and S3 = {(1), (12), (13), (23), (123), (132)} is the symmetric group of order 6 f(x) Ro, (1) R120 (12) R240 (13) Explain why f is not a homomorphism L (23) R120L R240L (123) (132)

Advanced Engineering Mathematics
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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Question 2. Consider the following function f: D3 → S3, Where D3 = {Ro, R120, R240, L, R1₁20L, R240L} is the dihedral group of order 6 and S3 = {(1), (12), (13), (23), (123), (132)) is the symmetric group of order 6 X Ro, f(x) (1) R120 (12) R240 (13) Explain why f is not a homomorphism L (23) R₁20L (123) R240L (132)
Transcribed Image Text:Question 2. Consider the following function f: D3 → S3, Where D3 = {Ro, R120, R240, L, R1₁20L, R240L} is the dihedral group of order 6 and S3 = {(1), (12), (13), (23), (123), (132)) is the symmetric group of order 6 X Ro, f(x) (1) R120 (12) R240 (13) Explain why f is not a homomorphism L (23) R₁20L (123) R240L (132)
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