Question about groups ?

1. Jul 23, 2011

cragar

1. The problem statement, all variables and given/known data
Does Euler's totient function tell me how many elements are in my group?

And once I know how many elements are in my group. the generators are the ones that are relatively prime with the number of element in my group.
Are my statements correct.

2. Jul 23, 2011

micromass

Staff Emeritus
Could you please clarify a bit? What group exactly are you talking about? Are you talking about the invertible elements of $\mathbb{Z}_n$??

3. Jul 23, 2011

cragar

I am talking about the elements in Z(star)n . so the elements in my group have no common factors other than 1 with n,

4. Jul 23, 2011

micromass

Staff Emeritus
Yes, the number of elements in 2n is indeed phi(n). With phi the Euler totient function.
But your statement of the generators is not true. It's very difficult to find generators for such a groups...

5. Jul 23, 2011

cragar

thanks for your help, my book is not very clear on how to find generators. Should I try to read another book on finding generators or make a Cayley table.