3. Let S3 act on the set A={(i,j) : 1≤i,j≤3} by σ((i, j)) = (σ(i), σ(j)). (a)...
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3. Let S3 act on the set A={(i,j) : 1≤i,j≤3} by σ((i, j)) =(σ(i), σ(j)).
(a) Describe the orbits of this action.
(b) Show this is a faithful action, i.e. that the permutationrepresen- tation φ:S3 →SA =S9
(c) For each σ ∈ S3, find the cycle decomposition of φ(σ) inS9.
3. Let S3 act on the set A={(i,j) : 1≤i,j≤3} by σ((i, j)) =(σ(i), σ(j)).
(a) Describe the orbits of this action.
(b) Show this is a faithful action, i.e. that the permutationrepresen- tation φ:S3 →SA =S9
(c) For each σ ∈ S3, find the cycle decomposition of φ(σ) inS9.
Answer & Explanation Solved by verified expert
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The solution to a is obtained by observing that the orbits ofany group action
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