What are the generators of Z2 x Z8?

The group ( \mathbb{Z}_2 \times \mathbb{Z}_8 ) can be generated by the elements ( (1, 0) ) and ( (0, 1) ). The element ( (1, 0) ) generates the subgroup ( \mathbb{Z}_2 ), while ( (0, 1) ) generates the subgroup ( \mathbb{Z}_8 ). Together, these two elements generate the entire group ( \mathbb{Z}_2 \times \mathbb{Z}_8 ). Thus, a generating set for this group is ( { (1, 0), (0, 1) } ).