This is a reference request for the following statement:

**Fact:**
Let $G$ be a reduced abelian $p$-group with an element of order $p^2$. Then $G$ contains an element of order $p$ and of finite height at least $1$.

The proof of this uses only basics properties of the height function $h_p(-)$ (and the result is trivial if $G$ has no elements of infinite height). However, instead of writing down the proof, I would prefer to make a reference to some textbook or paper, as I'm sure that this fact is well-known to specialists of abelian groups.