Let p be 1 mod 3 (separate question: work out 2 mod 3). What is the group structure of the abelian group $\mathbb{Q}_p ^* / \mathbb{Q}_p ^{*3}$?
$\mathbb{Q}_p ^*$ refers to the group of units in $\mathbb{Q}_p$, and $\mathbb{Q}_p ^{*3}$ is the group of units cubed.
I'm not really sure where to start with this. I believe the units in $\mathbb{Q}_p$ are just the non-zero elements. I can't seem to get a handle on $\mathbb{Q}_p ^{*3}$ though. Help and pointers would be much appreciated!