Generalized torsion elements in groups

2023/02/19 by Raimundo Bastos, Bastos, Raimundo, Csaba Schneider +3 · 1 citation
Materials Science · Mathematics · #20C15 #20E45 #20F12 #20F14 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2302.09589

openalex publication_date 2023/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• On the conjugacy class exponent of the finite simple groups

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