
Generators for Z/nZ
Dummit and Foote Section 1.2 Dihedral Groups Exercise 15 reads as follows:
Find a set of generators and relations for $\displaystyle \mathbb{Z}$/n$\displaystyle \mathbb{Z}$

If you particularize the problem to say $\displaystyle \mathbb{Z}$/4$\displaystyle \mathbb{Z}$ then 1 + 4$\displaystyle \mathbb{Z}$ is a generator and so is 3 + $\displaystyle \mathbb{Z}$.
But relations??? Are there any?
I guess then 1 + n$\displaystyle \mathbb{Z}$ is a generator for $\displaystyle \mathbb{Z}$/n$\displaystyle \mathbb{Z}$. Is that correct? Other generators? Relations???
Can someone please clarify and help?
Peter

Re: Generators for Z/nZ
Z/nZ is cyclic, so it has at least one generator, call it x. we only need to subject this generator to one relation to recover all the algebraic behavior of Z/nZ:
x^n = e.
(this is a really simple example, so don't overthink it).

Re: Generators for Z/nZ
Thanks
You write "this is a really simple example, so don't overthink it"
Good advice  I was looking for too much in it
Peter