How to prove that the direct product of group Z is not cyclic?
Hi, what exactly is not clear?
by definition, a cyclic group is a group that can be generated by a single element. As I understand, you ask whether is cyclic or not?
If were cyclic, then there would be an element such that every element can be written as for some integer . The proof in the previous post shows that if you choose any then there exists an element from such that no such exists. This contradicts the statement that is cyclic.