Here I've found two definitions of the rank of a $p$-group https://groupprops.subwiki.org/wiki/Rank_of_a_p-group. However, for the $2$-group $\mathbb{Z}/\mathbb{Z}_{4}$, the rank with the first definition would be $2$ but if I'm not wrong with the second it would be $1$. So my question is: am I wrong or is the webpage wrong?
I think that the second definition might be something like the maximum $r$ for which there exists an abelian subgroup such that the minimum size of a generating set whose elements have order $p$ is $r$. Would this be right?
The rank of $\mathbb Z/4\mathbb Z$ is $1$ as the only elementary abelian subgroup is $2\mathbb Z/4\mathbb Z$ which has order $2^1$.