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October 19th, 2016, 01:51 PM   #1
AR1
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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 .
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October 23rd, 2016, 03:21 AM   #2
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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.
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October 23rd, 2016, 06:08 AM   #3
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Quote:
Originally Posted by Country Boy View Post
Do you know what "cyclic" means?
I sure haven't missed your bolding in your absence.
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