Explore the intricacies of commutator subgroups and subalgebras in toric topology through a 31-minute lecture delivered by Fedor Vylegzhanin from NRU Higher School of Economics. Scheduled for August 19, 2024, as part of the Workshop on Toric Topology and the Focus Program on Toric Topology, Geometry and Polyhedral Products at the Fields Institute, this talk delves into advanced mathematical concepts within the field of toric topology. Gain insights into the speaker's research and findings, connecting the dots between commutator structures and their applications in this specialized area of mathematics.