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.