Let (G,·) be a finite group, and let S be a set with the same
cardinality as G. Then there is a bijection μ:S→G . We can give a
group structure to S by defining a binary operation *on S, as
follows. For x,y∈ S, define x*y=z where z∈S such that μ(z) =
g_{1}·g_{2}, where μ(x)=g_{1} and μ(y)=g_{2}.
First prove that (S,*) is a group.
Then, what can you say about the bijection μ?