Finite axiomatizability of the rank and the dimension of a pro-$\pi$ group

Martina Conte, Benjamin Klopsch

The Prüfer rank $\mathrm{rk}(G)$ of a profinite group $G$ is the supremum, across all open subgroups $H$ of $G$, of the minimal number of generators $\mathrm{d}(H)$. It is known th…