Originally Posted by
Swlabr I'm a bit confused as to what the question is asking here - is it saying "$\displaystyle (Z/p^2)^x \cong C_p \times C_{p-1} \cong C_{p(p-1)}$"? That is, $\displaystyle \underbrace{(Z/p^2) \times (Z/p^2) \times \ldots \times (Z/p^2)}_\textrm{x times} \cong C_{p(p-1)}$?
If so, I don't think I believe this. $\displaystyle C_{p(p-1)}$ is finite, but if this is isomorphic to the direct product of $\displaystyle Z/p^2$ with itself an arbitrary number of times we get that $\displaystyle C_{p(p-1)} \cong C_{p(p-1)} \times C_{p(p-1)}$, a contradiction...
I am willing to be proved wrong though.