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Definition: Given two groups G and H, there are several ways to form a new group. The simplest is the direct product, denoted GxH. As a set, the group direct product is the Cartesian product of ordered pairs (g,h), and the group operation is componentwise, so (g_1,h_1)x(g_2,h_2)=(g_1g_2,h_1h_2).