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2.11. The group S3 consists of the following six distinct elements e, σ, σ’, τ, στ, σετ, where e is the identity element and multiplication is performed using the rules 0³ = e, 7² = 1, TO = = 0²T. Compute the following values in the group S3: (a) To² (c) (OT) (OT) (b) τ(στ) Is S3 a commutative group? (d) (OT)(0²T).

2.11. The group S3 consists of the following six distinct elements e, σ, σ’, τ, στ, σετ, where e is the identity element and multiplication is performed using the rules 0³ = e, 7² = 1, TO = = 0²T. Compute the following values in the group S3: (a) To² (c) (OT) (OT) (b) τ(στ) Is S3 a commutative group? (d) (OT)(0²T).

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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2.11. The group S3 consists of the following six distinct elements e, σ, σ’, τ, στ, σετ, where e is the identity element and multiplication is performed using the rules 0³ = e, 7² = 1, TO = = 0²T. Compute the following values in the group S3: (a) To² (c) (OT) (OT) (b) τ(στ) Is S3 a commutative group? (d) (OT)(0²T).
Transcribed Image Text:2.11. The group S3 consists of the following six distinct elements e, σ, σ’, τ, στ, σετ, where e is the identity element and multiplication is performed using the rules 0³ = e, 7² = 1, TO = = 0²T. Compute the following values in the group S3: (a) To² (c) (OT) (OT) (b) τ(στ) Is S3 a commutative group? (d) (OT)(0²T).
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