two questions. First, what is a group of transformations? I know what it is, but how do i enumerate the elements? i.e, let T be the set of all functions such that f(x) = x, 2x, what? The question asks me to find a group of transformations isomorphic to the group of integers mod 8 under addition. I know what that means. it means find a function,phi, that is a bijection between my group and the transformation group. BUT what is that function if i don't even know the elements in the transformation group. can i use the function in the trans. group for my phi or what?
second question: if a cyclic group G is generated by "a" of order m, prove that the powers of a^k generate all of G iff gcd (k,m)=1. I just need help with it. or a hint.