- #1

mathjam0990

- 29

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**Is the group R^{x} isomorphic to the group R? Why?**

__Question:__R^{x} = {x ∈ R | x not equal to 0} is a group with usual multiplication as group composition. R is a group with addition as group composition.

Is there any subgroup of R^{x} isomorphic to R?

**Sorry, I would have liked to show some steps I took, but Not sure where to begin. I tried, but couldn't get too far. Or well, I can say I know for something to be isomorphic the function should be,**

__What I Know:__1)Injective

2)Surjective

3)Homomorphism f(ab)=f(a)f(b) for all a,b in group

Do I just show that all elements in real numbers with multiplication defined maps to real numbers has those 3 properties above?

Thank you!