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