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 October 9th, 2017, 02:03 PM #1 Member   Joined: Jan 2015 From: usa Posts: 92 Thanks: 0 semi-product I need your help to prove the folowing problem: Let $G$ be a group and $N$ a normal subgroup of $G$ such that $G/N\cong\mathbb{Z}$. Show that $G=N⋉C$ for some subgroup $C$ of $G$.
 October 9th, 2017, 06:17 PM #2 Member   Joined: Jan 2016 From: Athens, OH Posts: 79 Thanks: 39 Mona, This is my last reply to one of your posts until I get some feedback from you on whether my response allowed you to finish the problem. If you can't solve the problem from my hint(s), just ask for more help; otherwise just say "got it". Let G/N=. Then it should be easy to prove that G is the semi direct product of N and . Thanks from topsquark
 October 10th, 2017, 12:15 AM #3 Member   Joined: Jan 2015 From: usa Posts: 92 Thanks: 0 it is $N\rtimes C$, i am sorry
 October 10th, 2017, 03:19 PM #4 Member   Joined: Jan 2016 From: Athens, OH Posts: 79 Thanks: 39 Did you not understand that I was saying to set C = , the cyclic subgroup of G generated by x where G/N = . Here xN is any generator of the cyclic group G/N.

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