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

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- Anonymous2 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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