Beyond coclass

Abstract

Abstract The primary step in classifying the finite p-groups of coclass at most p lies in the classification of infinite pro-p-groups of coclass at most r. The question then arises as to what other classes of pro-p-groups can be used for finding other classifications of finite p-groups. At this point the pro-p-groups become at least as interesting as the finite p-groups. The conditions to be imposed on the pro p-groups are generally finitistic, and hence apply vacuously to finite p-groups.