In mathematics, a group $G$ is called free if there is a subset $S$ of $G$ such that any element of $G$ can be written in one and only one way as a product of finitely many elements of $S$ and their inverses.
The group $(\mathbb{Z},+)$ of integers is free; we can take $S = \{1\}$. ("Free group", Wikipedia)
By saying "product of finitely many elements of $S$ and their inverses", in case of $(\mathbb{Z},+)$, does product refer to $+$?
If not, can anyone correct misunderstanding?