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Let γ and δ be the following elements of the permutation group:γ = (35412) δ =...

Let γ and δ be the following elements of the permutation group:γ = (35412) δ = (314)(25).

a.) Calculate: (1) γ ◦ δ, (2) δ ◦ γ, (3) δ−1 and (4) γ−1.
b.) Do γ and δ commute?
c.) Prove that γ generates a group isomorphic to (Zn,+n) for some n. d.) Prove that δ generates a group isomorphic to (Zn,+n) for some n. e.) Prove that β = (123)(456) does not generate a group isomorphic to (Zn, +n) for any n.

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