its advance groups theory

a. Consider Z= a~be a-b = 0;a=b(mod52) . Interpret that ~ is an equivalence relation. 52 b. Let $2 = 1,2,3; and G= Z,. List all possible actions are there of G on $2 If G = Z,, then what would happen? c. Let f : A-> B be a G-morphism. If A, is an orbit in A, then show that f (A ) is an orbit in B