Generalized Torsion Elements as Generalizations of Torsion Elements

Explore the concept of generalized torsion elements in group theory through this 48-minute lecture by Tetsuya Ito from Kyoto University. Delve into the definition of generalized torsion elements as those where a product of their conjugates equals the identity. Examine how these elements serve as obstructions to bi-orderability in groups. Investigate various notions of generalized torsion, including groups where generalized torsions are torsion and groups entirely composed of generalized torsion elements. Learn about the connection between generalized torsion elements and the Alexander polynomial, including a method for determining lower bounds on their order. Gain insights into the relationship between this concept and bi-orderability criteria based on the Alexander polynomial. This talk is part of the Workshop on Orderable Groups held at the Centre de recherches mathématiques (CRM) in May 2023.