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)).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 22E

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