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As I am sure some of you may have noticed I'm doing a series of exercises by Rotman and I am finding difficulties. Now I unbeaten into this problem

Give an example of an abelian and a non-abelian group with isomorphic automorphism groups.

Can you help me?

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    Please don't yell.2011-05-19

1 Answers 1

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Try $A=\mathbb{F}_2^2$, and $G=S_3$.

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    @Pete L.Clark . You're right, I'm taking the first steps in group theory, and so I asked for help not complete resolution exercise. In this type of exercises I can use brute force, in the sense that I am able to find all automorphisms of a group and then subsequent comparisons, the fact is that to find an example it took me a long time, then I'm asking whether there is indeed a theorem, or more, which allows me to limit the search to the types of groups2011-05-20