I found the following problem in my book:
For $n \in N, n \geq 2,$ define $\mathbb = Z {[x] : [x] \in \mathbb Z _n; gcd(x,n)=1}$ Prove that $( \mathbb Z ^x _n , \odot)$ is a group.
Perhaps what is confusing me most is the symbol $ \odot$, which I can't seem to place. There is no further instruction for this problem.
However I do not know why it needs to be specified that $gcd(x,n)=1$ here, as I can only figure that that means x can't be a multiple of or be divisible by multiples of n. I'm aware that right identity and right inverse implies that it is a group, and vice versa I believe,