Abstract Algebra HW Question

  • Thread starter Kuzu
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  • #1
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I'm taking this course "abstract algebra" at university and I've been given some homework questions. I was able to solve all of them but one. And it would be great if anyone could help me with this.

The question is like this:
"If all cyclic subgroups of G are normal, then show that all subgroups of G are normal"


as I know all cyclic groups are abelian, and G itself is a subgroup of G so it is cyclic and abelian. Also I know that every subgroup of an abelian group is normal. So I didn't even understand the question completely.

How can I solve this?
 

Answers and Replies

  • #2
Dick
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Try a proof by contradiction. Take H to be a subgroup of G and suppose H is not normal. What does that tell you?
 

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