Consider the group $\mathbb{Q}$ under addition of rational numbers. If $H$ is a subgroup of $\mathbb{Q}$ with finite index, then $H = \mathbb{Q}$.
I just saw this on our exam earlier and was stumped on how to show this. Any ideas?
Consider the group $\mathbb{Q}$ under addition of rational numbers. If $H$ is a subgroup of $\mathbb{Q}$ with finite index, then $H = \mathbb{Q}$.
I just saw this on our exam earlier and was stumped on how to show this. Any ideas?