Overview: The course aims to introduce young researchers to the theory of profinite and pro-p groups (where p denotes a prime number). Profinite groups originated from Galois theory, as every Galois group is profinite, yet profinite and pro-p groups show up in several contexts.
In particular, the impetus for current research on pro-p groups could be broadly described as coming from four directions: number theory; the problem of classifying finite p-groups; the theory of infinite groups; profinite group theory “in its own right”. The goal of the course is to
give a comprehensive background on profinite and pro-p groups, and some examples of how the study of these groups may lead to results in the aforementioned branches of Algebra.