Find all group morphism from ( Z,+) to (Q, +)

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Homework Help Overview

The discussion revolves around finding all group morphisms from the group of integers (Z, +) to the group of rational numbers (Q, +). Participants are exploring the properties and characteristics of homomorphisms in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the identity morphism and express uncertainty about identifying all possible morphisms. There are inquiries into the properties of homomorphisms from (Z, +) and suggestions to consider relevant theorems or descriptions that could aid in identifying these morphisms.

Discussion Status

The discussion is active, with participants sharing thoughts on the nature of homomorphisms and considering theorems related to free Abelian groups. Some guidance has been offered regarding the exploration of descriptions that could simplify the identification of morphisms.

Contextual Notes

There is an indication that participants may be working under constraints related to their understanding of homomorphisms and the properties of the groups involved.

polarbears
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Homework Statement


Find all group morphism from ( Z,+) to (Q, +)


Homework Equations


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The Attempt at a Solution


I think the identity morphism is included, but I'm not sure what else
 
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Don't you know a lot about homomorphisms whose domain is (Z,+)?
 
Well I think the trouble I'm having is finding all of them
 
Which is why you need to consider what facts you know about homomorphisms from (Z,+)!

Surely you know some useful theorem about homomorphisms from free Abelian groups?

And if not, you could look find some easy way to describe any such homomorphism, and maybe this description would make it easy to identify all of them.
 
f(n)=cn

wow that was pretty obvious...I need some rest

thanks for the help!
 

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