How to Find the Subgroup of a Quotient Group with a Given Generator?

[physix123]

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!

 

[daveyinaz]

Given a generator of the subgroup? Just enumerate the elements you obtain by performing the group's operation on the generator until you get the identity...or am I misunderstanding what you are asking...?