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 using its character table.
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