For context, I'm starting to learn group theory, and one question is "Is $(\mathbb{Q}^\times, \cdot)$ a group?" Not looking for help with the question, just wondering what $\mathbb{Q}^\times$ means.
If it was by itself, I would have assumed rationals with multiplication, but it just seems to be a set. My next guess is rationals without zero, is that correct?
For a commutative ring $R$ often the group of units is denoted by $R^{\times}$, or also by $U(R)$. In the case when $R$ is a field, it coincides with $R\setminus 0$.
For example, $\Bbb Z[i]^{\times}=\{1,-1,i,-i \}$ and $\Bbb Q(i)^{\times}=\Bbb Q(i)\setminus 0$. Or $\Bbb Z^{\times}=\{1,-1\}$ and $\Bbb Q^{\times}=\Bbb Q\setminus 0$.