Let X be a set, and let Y⊆X. Show that the subset of S_{x} consisting of all f such that f(y)=y for all y∈Y forms a subgroup
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Originally Posted by hzhang610 Let X be a set, and let Y⊆X. Show that the subset of S_{x} consisting of all f such that f(y)=y for all y∈Y forms a subgroup You need to confirm all the properties for being a subgroup are satisfies. Show what you did.
i) it is closed under the operation. Let y₁,y₂∈Y , then f(y₁)f(y₂)=y₁,y₂ ii) it is closed under inverses. Let y∈Y,???
Originally Posted by hzhang610 ii) it is closed under inverses. Let y∈Y,??? Try this. Let be a permutation leaving fixed. Since it is a bijection it means there is an inverse permutation, . Argue this inverse permutation is what you are looking for as an inverse.
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