A profinite group is called strongly complete if every subgroup of finite index is open. Strongly complete groups are very useful, since in such groups the algebra determines the topology. For example, every homomorphism from a strongly complete group to any profinite group is continuous, and thus a homomorphism in the category of profinite groups. For many years it was an open question, whether every finitely generated profinite group is strongly complete. In 2000 Segal and Nikolov published a positive proof for this conjecture. In the talk we present the general idea of the proof, and show some nice results relying on this theorem.
This video was produced by Tel Aviv University as part of its algebra seminar.
