Let A = {1, 2, 3, 4, 5} and S = A³.Define an action o : S5 × S → S(σ(a₁), σ(a2), σ(a3)),by σo(a₁, a2, az)σ € S5, (a₁, A2, A3) € S.(i)=Is this action transitive ? Justify youranswer.(ii) Find the stabiliser of (1, 2, 3) € S.

Given : A=1, 2, 3, 4, 5 and S=A3 Define an action o : S5×S→S by σ o a1, a2, a3=σa1, σa2, σa3,…

Answered: Let A = {1, 2, 3, 4, 5) and S = A³.…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 27EQ

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Let A = {1, 2, 3, 4, 5) and S = A³. Define an action o : S5 × S → S by σο(a1, 22, ag) (σ(a₁), σ(a₂), σ(ªz)), σ € S5, (a₁, 82, 83) € S. (i) = Is this action transitive ? Justify your answer. (ii) Find the stabiliser of (1, 2, 3) € S.