I am learning for my exams and came by the topic factor groups. I know what a Normal subgroup is and how $\mathbb{Z}/n\mathbb{Z}$ for $(\mathbb{Z}, +)$ looks. However, how does the Group $\mathbb{Q*}/\mathbb{Q}_{x>0}$ with $(\mathbb{Q}/\{0\}, *)$ look like? Is it just $1$ and $-1$?
And how are factor groups usefull?
Kind Regards