i am confused about how to find the subgroup of a quotient group given a generator. for example, a lot of problems give as the group Z/nZ with n very large. how do you find the subgroup given a generator?
thanks!
i am pretty sure it's true that to find the order of a permutation, you can find LCM of the length of the disjoint cycles...
if you have a permutation that doesn't have disjoint cycles (i.e. like one with (1,3,6,8)(4,6)), then can you use the same method to find the order? I feel like I am...