Example Generated groups Letg=z,=(1, 2, 3, 4, 5, 6 =the multiplicative group modulo 7 Leth=(1, 2, 4(mod 7)... a subgroup of G Let s=(2 Then <2>=(2) for integers i 23=1 implies that <2>=(1, 2, 4=H 2 generates the subgroup H ofgGenerated Groups Example Let G = Z*7 = {1,2,3,4,5,6} = the multiplicative group modulo 7 Let H = {1,2,4} (mod 7) … a subgroup of G Let S = {2}. Then <2> = {2i} for integers i 2 3 = 1 implies that <2> = {1,2,4} = H 2 generates the subgroup H of G