# Thread: Does the group U(12) of units in Z/12 have the same structure as U(8)?

1. ## Does the group U(12) of units in Z/12 have the same structure as U(8)?

Does the group U(12) of units in Z/12 have the same structure as U(8)?

I don't quite understand the question.
Could you please explain what it means by "units" and by "structure"?

2. Originally Posted by feyomi
I don't quite understand the question.
Could you please explain what it means by "units" and by "structure"?
A group of units is the group of elements another group that have an inverse.

So in $\mathbb{Z}/12\mathbb{Z}$, the group of units, or how you denote it $U(12) = \{1,5,7,11\}$.

3. Originally Posted by chiph588@
A group of units is the group of elements another group that have an inverse.

So in $\mathbb{Z}/12\mathbb{Z}$, the group of units, or how you denote it $U(12) = \{1,5,7,11\}$.

How would I go about determining whether there is a correspondence between the two groups at hand?

4. Originally Posted by feyomi
How would I go about determining whether there is a correspondence between the two groups at hand?
Do, what's obvious. Since $\varphi(12)=\varphi(8)=4$ draw out the two Cayley tables (not really but you get the idea) and figure out the isomorphism.