Generalized torsion elements in groups

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 $G$ using its character table.

11 pages

References in corpus (2)

• Strong reality of finite simple groups
• On a group whose generalized torsion elements are torsion elements

Cited by in corpus (1)

• Generalized torsion elements in infinite groups