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arXiv · 2302.09589

Generalized torsion elements in groups

Raimundo Bastos·Csaba Schneider·Danilo Silveira
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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.

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Raimundo Bastos, Csaba Schneider, Danilo Silveira. 2023-02-19. Generalized torsion elements in groups. https://doi.org/10.1007/s00013-023-01931-5

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