Example S subgroups Letg=z 7=(1, 2, 3, 4, 5, 6 =the multiplicative group modulo 7 Let h=(1, 2, 4)(mod 7).. a subset ofG 1. h is closed under multiplication modulo 7 2. I is still the identity 3. 1 is 1 inverse. 2 and 4 are inverses of each other 4. associativity still applies 5. commutativity still applies H is a subgroup ofgSubgroups Example Let G = Z*7 = {1,2,3,4,5,6} = the multiplicative group modulo 7 Let H = {1,2,4} (mod 7) … a subset of G Note: 1. H is closed under multiplication modulo 7 2. 1 is still the identity 3. 1 is 1 inverse, 2 and 4 are inverses of each other 4. associativity still applies 5. commutativity still applies H is a subgroup of G