Proving Isomorphic Groups U(5) and U(10)

[gtfitzpatrick]

Homework Statement

For any positive integern, let U(n) be the group of all positive integers less than n and relatively prime to n, under multiplication modulo n. Show the the Groups U(5) and u(10) are isomorphic

Homework Equations

The Attempt at a Solution

any 2 cyclic groups of the same size have to be isomorphic.
For the answer to this problem should i do out a caley table for both groups to show they are cyclic? is this enough along with my statement? i guess what I am saying is...does the question ask me to prove that 2 cyclic groups of the same size are isomorphic?

 

[micromass]

No, a Cayley table would be overkill! (although it would work).

I suggest you first work out what U(5) and U(10) is explicitely. Try to prove that they have the same order.
Then try to find a cyclic element in both groups.