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

Answer 1

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.

Source(s): https://math.stackexchange.com/questions/1097628/p...