1. The problem statement, all variables and given/known data Show ZXZ is an infinite cyclic group. Under addition of course. 2. Relevant equations 3. The attempt at a solution So this obviously is an infinite cyclic group. Z is generated by <1> or <-1>. The problem I run into here is I think <(1,1)> will only generate elements of the form (a,a) s.t. a is an element of Z, (think along the diagonal). I do not see a way to generate something like (2,3).