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)).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...

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