Actually I have solved the part "Inn(S3)≃S3" by using the result-
"Let G be a group. Then GZ(G)≃Inn(G), where Z(G)={g∈G∣gx=xg∀x∈G}"
So I put G=S3 and hence Z(S3)={e}, where e is identity permutation.
And thus S3Z(S3)≃S3
Finally, using the above result, we get, Inn(S3)≃S3.
But how to prove Aut(S3)≃S3. Although, One thing I have notice that, to prove Aut(S3)≃S3, it is enough to show that Inn(S3)≃Aut(S3). But I am stuck with it also.
Can anyone suggest me a clear and rigorous wayout?
Thanks for your help in advance.
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