if there is one to one correspondence between two sets A and B. Then show that Sym(A)=Sym(B)?

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  • Anonymous
    2 months ago

    Take a bijection

    f:A→B

    Now take a permutation σ∈Sym(A)

    Show that f∘σ∘f−1 is a permutation of B

    .And then show that the map

    Sym(A)→Sym(B),

    taking σ to f∘σ∘f−1 is a bijection.

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