What is the function/symbol to represent the set of Coprimes?

Question

Just wondering if there’s an established symbol or function used to represent the set of coprimes of N which are less than or equal to N?

Thanks!

Answer 1

These make up the group of units of the ring $\mathbb{Z}/ N\mathbb{Z}$ and this can be denoted sometimes as $U(\mathbb{Z}/ N\mathbb{Z}), \mathbb{Z}/ N\mathbb{Z}^*, \mathbb{Z}/ N\mathbb{Z}^{\times}$ and sometimes in German texts we get $E(\mathbb{Z}/ N\mathbb{Z})$.

Technically this is a group under multiplication modulo $N$ and so comes with greater structure than a set but I'm sure you could use it just as a set.

EDIT: It was pointed out in the comments that in fact $\mathbb{Z}/ N\mathbb{Z}$ is a quotient group of the integers and so its members are not, strictly speaking, integers but rather equivalence classes under the "modulo $N$" relation. However, it is common to choose representatives for these classes between $0$ and $N-1$ and so, if you make that clear, the above should still be fine.