Generalized torsion elements in infinite groups

In this talk we present some properties of generalized torsion elements in groups. We describe the set of generalized torsion elements in finitely generated abelian-by-finite groups. In addition, we present a family of Bieberbach groups in which every element is a generalized torsion element. This presentation is mainly based in the following papers [1,2,3]. 

There will be a coffee break after the seminar.

References

[1] R. Bastos and L. Mendonça. Generalized torsion elements in infinite groups. arXiv:2411.17918 [math.GR]. 

[2] R. Bastos, C. Schneider and D. Silveira. Generalized torsion elements in groups.  Arch. Math. (Basel)  122 (2024),  121--131.  

[3] G. Naylor and D. Rolfsen. Generalized torsion in knot groups. Canad. Math. Bull. 59  (2016), 182--189.