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October 19th, 2016, 01:51 PM  #1 
Newbie Joined: Oct 2016 From: USA Posts: 2 Thanks: 0  Prove function is cyclic with generator help
How do I show that the group is cyclic with generator Θ(g). Θ(G)={Θ(x) x∈G} if: G and G′ be groups and let Θ : G → G′be a homomorphism. Assume G is cyclic with generator g . 
October 23rd, 2016, 03:21 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,217 Thanks: 555 
Do you mean: "if G is a cyclic group. with generator g, and there exist a homomorphism Θ such that G'= Θ(G), then G' is also cyclic with generator Θ(g)"? As I said in the previous thread, this follows pretty much from the basic definitions. Do you know them? Since you have shown no attempt yourself to do this problem, that is not clear. Do you know what "cyclic" means? Do you know what "homomorphism" means? (And how a "homomorphism" is different from an "isomorphism"?). Write out those definitions and think about how to apply them. 
October 23rd, 2016, 06:08 AM  #3 
Senior Member Joined: Feb 2016 From: Australia Posts: 728 Thanks: 274 Math Focus: Yet to find out.  

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cyclic, function, generator, prove 
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