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Math Help - prove for subgroup

  1. #1
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    prove for subgroup

    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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  2. #2
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    Quote Originally Posted by hzhang610 View Post
    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.
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  3. #3
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    I did the first part

    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,???
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  4. #4
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    Quote Originally Posted by hzhang610 View Post
    ii) it is closed under inverses.
    Let y∈Y,???
    Try this. Let \sigma be a permutation leaving y\in Y fixed. Since it is a bijection it means there is an inverse permutation, \sigma^{-1}. Argue this inverse permutation is what you are looking for as an inverse.
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