Read: Read 3.2–3.3.2.
Turn in: 3.33, 3.36, 3.37, 3.39, 3.40, 3.43, 3.44
- In problems 3.36 and 3.37, you are asked to prove the subsets $G$ and $U$ of $\mathbb{H}$ are groups. The first thing to address is why $G$ and $U$ are closed under multiplication from $\mathbb{H}$. Another thing to address is why multiplication is associative with respect to $G$ and $U$, but you don’t need to prove this one because multiplication is already known to be associative with respect to the larger set $\mathbb{H}$ (and you can just state that).
Please try (but do not turn in): 3.34, 3.38
