I have questions about constructing a group structure, how to identify the order of a paired group when they have different orders and method of figuring out the group identity and the inverse of a pair that contained in the paired group.
If G and H are groups then explain how to equip G x H with a group structure. If G has order k and H has order m then what is the order of G x H? What is the group identity and the inverse of an element (g, h) Є G x H.