Consider S3 = the set of all permutations on the set [3]. You can find these 6 permutations in the notes. Determine each of the following sets. (a) {x^2: x ∈ S3} (b) {x ∈ S3 : x^2 = e} (c) C(α) = {g ∈ S3 : gα = αg}, where α = (1 3) (d) Z(S3) = {g ∈ S3 : ga = ag for all a ∈ S3}

Consider S3 = the set of all permutations on the set [3]. You can find these 6 permutations in the notes. Determine each of the following sets. (a) {x^2: x ∈ S3} (b) {x ∈ S3 : x^2 = e} (c) C(α) = {g ∈ S3 : gα = αg}, where α = (1 3) (d) Z(S3) = {g ∈ S3 : ga = ag for all a ∈ S3}

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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Question

Consider S3 = the set of all permutations on the set [3]. You can find these 6 permutations in
the notes. Determine each of the following sets.
(a) {x^2: x ∈ S3}
(b) {x ∈ S3 : x^2 = e}
(c) C(α) = {g ∈ S3 : gα = αg}, where α = (1 3)
(d) Z(S3) = {g ∈ S3 : ga = ag for all a ∈ S3}

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