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(a) Find the conjugacy classes of Qg. (b) Find the conjugacy classes of S3. (c) Is the action by conjugation on Qg faithful? How about S3? Explain.

(a) Find the conjugacy classes of Qg. (b) Find the conjugacy classes of S3. (c) Is the action by conjugation on Qg faithful? How about S3? Explain.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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20. Let G be a group and let G act on itself by conjugation. For a e G, denote Oa the orbit of a under conjugation action. The orbits under the conjugation action are called the conjugacy classes of G. (a) Find the conjugacy classes of Qg. (b) Find the conjugacy classes of S3. (c) Is the action by conjugation on Q8 faithful? How about S3? Explain.
Transcribed Image Text:20. Let G be a group and let G act on itself by conjugation. For a e G, denote Oa the orbit of a under conjugation action. The orbits under the conjugation action are called the conjugacy classes of G. (a) Find the conjugacy classes of Qg. (b) Find the conjugacy classes of S3. (c) Is the action by conjugation on Q8 faithful? How about S3? Explain.
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