Find all the abelian groups of order $2100.$ For each group, give an example of an element of order $210.$
$2100 = 2^2 \cdot 3 \cdot 5^2 \cdot 7,$ then
$G_1 = \mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb Z_3 \times \mathbb{Z}_5 \times \mathbb{Z}_5 \times \mathbb{Z}_7 \cong \mathbb Z_{10}...