In this talk we present some properties of generalized torsion elements in groups. Moreover, we try connect this "new'' concept with the usual concept of torsion in some standard class of groups (e.g., nilpotent, FC-groups). This presentation is mainly based in the following papers [1,2,3,4]. This is joint work with C. Schneider and D. Silveira.   
      

References

[1] R. Bastos, C. Schneider and D. Silveira. Generalized torsion elements in groups.  To appear in Arch. Math. Basel (2023), arXiv:2302.09589.  

[2] G. Endimioni. On certain classes of generalized periodic groups. Ischia Group Theory 2006 (2007), 93-102.

[3] T. Ito. On a group whose generalized torsion elements are torsion elements. To appear in Comm. Alg. (2023), arXiv:2303.05726v2.

[4] G. Naylor and D. Rolfsen. Generalized torsion in knot groups. Canad. Math. Bull. 59 (2016), 82-189.