I have a question about Quotient groups. I have a task to find a quotient group $G/H$ of group $G = 15\mathbb{Z}_{18}$ by $H = 8\mathbb{Z}_{18}.$
$G = \{0, 3, 6, 9, 12, 15, 18, 21\}$
I found that $G / H = \{8\mathbb{Z}_{18}, 3 + 8\mathbb{Z}_{18}, 6 + 8\mathbb{Z}_{18}, 9 + 8\mathbb{Z}_{18}, 2 + \mathbb{Z}_{18}, 5 + 8\mathbb{Z}_{18}, 8 + \mathbb{Z}_{18}, 1 + 8\mathbb{Z}_{18}\}$.
Let $a = 3 + 8\mathbb{Z}_{18}, b = 5 + 8\mathbb{Z}_{18} \Rightarrow aH + bH = (a + b) + H = 8 + 8\mathbb{Z}_{18}$. Is it isomorphic to $\mathbb{Z}_8$?
So, is it fine solution or not?