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Starting from the group of automorphisms of $C_{2^{n}}$ find the automorphism $x$ of order 2 (with $n\geq 3$) and building the semidirect product $C_2$ and $C_{2^{n}}$ by $y$, where $y$ is an application of $C_2$ into $x$.

Can you help me?

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    "... and building the semidirect product..." *what*? You have a dangling clause there. What is one supposed to do by building the semidirect product?2011-05-26
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    "Can you help me?" Not right now, because you didn't say what you need help with. If by "help" you mean solve the exercise for you, then again the answer is "no", because that's not the point of the exercise. By the way, "find _the_ automorphism" should probably read "find _an_ automorphism", since there are 3 of them.2011-05-26
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    To get automorphisms of order 2, ref. "A classical Introduction to Modern Number Theory", chapter 4, and to construct semidirect products, up to isomorphism, refer "Groups and Representations"-Alperin,Bell; a section on "Semidirect Products".2011-05-28

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