Noncommutative Rings and applications

Next Seminar

Date:  November 18, 2025

Time: 15:00 (São Paulo Time: UCT-3) 

Location: IME, Room A242

Speaker: Claude Marion (IME-USP)

Title:  The pro-V topology on a free group: deciding denseness and closedness

Abstract: 

Given a free group F and a pseudovariety V of finite groups (i.e. a class of finite groups closed under subgroups, quotients and finite direct products), the pro-V topology on F is the smallest topology such that every homomorphism from F to any element of V is continuous, where finite groups are given the discrete topology. Two equivalent open problems are:  when V is the class S of all finite solvable groups, is it decidable whether an arbitrary finitely generated subgroup of F is dense (respectively, closed)?  In this talk we will investigate related problems for other pseudovarieties V (most of them) sitting in S. This is joint work with Pedro V. Silva and Gareth Tracey.