# Let G be Sn, the symmetric group of order n, acting as permutations on the set {1,2,...n}. Let H =?

Let G be Sn, the symmetric group of order n, acting as permutations on the set {1,2,...n}. Let H = {sigma element in G | n * sigma = n}.
(i) Prove that H is isomorphic to Sn-1.
(ii) Find a set of elements a1,...,an element in G such that Ha1,...,Han give all the right cosets of H in G.
(iii) Find the...
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Let G be Sn, the symmetric group of order n, acting as permutations on the set {1,2,...n}. Let H = {sigma element in G | n * sigma = n}.

(i) Prove that H is isomorphic to Sn-1.

(ii) Find a set of elements a1,...,an element in G such that Ha1,...,Han give all the right cosets of H in G.

(iii) Find the coset representation of G by H.

Not sure with proof. Please help!

(i) Prove that H is isomorphic to Sn-1.

(ii) Find a set of elements a1,...,an element in G such that Ha1,...,Han give all the right cosets of H in G.

(iii) Find the coset representation of G by H.

Not sure with proof. Please help!

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