Let $G,H$ be two groups. Show that the order of $G$, $|G| = 16$.

Question

Let $G = U(\mathbb{Z}_{32})$ and let $H = \big\{[1],[31]\big\} \leq G$.

(i) Show that $|G| = 16$.

Answer 1

The invertible elements are the odd ones, which of course are exactly $16$. I fail to see the relevance of $H$.