Constructing CF Groups by Coclass

Abstract

A pro-$p$-group is a CF group if all (except possibly the first) of its lower central series factors have order $p$. We describe a construction for a class of just-infinite CF pro-$p$-groups with fixed coclass. Based on that, we observe that the class of infinite CF pro-$p$-groups is comparatively large within the class of all just-infinite pro-$p$-groups of fixed coclass.