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Question: 5 let g be a group of permutations not necessarily...

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5. Let G be a group of permutations (not necessarily all of S.) of [n] = {1, 2, ,n) .., nj. Define the stabilizer of an element i E [n] to be In other words, Gi is the set of permutations in G fixing i (a) Show that Gi is closed under the group operation, i.e., if α, β Gi, then αβ E Gi. (b) Show the identity permutation is in G, (c) Show that Gi is closed under inverses, ie., ifa є Gi, then α-e Gi. The above establishes that Gi is a subgroup of G.

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