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Definition: The free product G*H of groups G and H is the set of elements of the form g_1h_1g_2h_2...g_rh_r, where g_i in G and h_i in H, with g_1 and h_r possibly equal to e, the identity element of G and H. Free products of more than two groups are defined recursively, i.e., G_1*G_2*...*G_n=(G_1*G_2*...*G_(n-1))*G_n. The free group F_n is the free product of Z with itself n times.