English

Generalized torsion elements in groups

Group Theory 2025-08-28 v1

Abstract

A group element is called a generalized torsion if a finite product of its conjugates is equal to the identity. We prove that in a nilpotent or FC-group, the generalized torsion elements are all torsion elements. Moreover, we compute the generalized order of an element in a finite group GG using its character table.

Keywords

Cite

@article{arxiv.2302.09589,
  title  = {Generalized torsion elements in groups},
  author = {Raimundo Bastos and Csaba Schneider and Danilo Silveira},
  journal= {arXiv preprint arXiv:2302.09589},
  year   = {2025}
}

Comments

11 pages

R2 v1 2026-06-28T08:43:51.511Z