Let S3 act on Ω = S3 by conjugation, and let θ : S3 → S6 be the resultinghomomorphism (see the previous problem). Label each element of Ω with1, ..., 6, and explicitly give θ((1 2 3)). Could you have done this problemmore easily if you had used the Cayley digraph of this action given inFigure 4.4? Use the Cayley digraph to give θ((1 2)).

Let S3 act on Ω = S3 by conjugation, and let θ : S3 → S6 be the resultinghomomorphism (see the previous problem). Label each element of Ω with1, ..., 6, and explicitly give θ((1 2 3)). Could you have done this problemmore easily if you had used the Cayley digraph of this action given inFigure 4.4? Use the Cayley digraph to give θ((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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