Generalized torsion orders of generalized torsion elements

2023/10/04 by Tetsuya Ito, Ito, Tetsuya
Computer Science · Materials Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Matrix Theory and Algorithms #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2310.02577

openalex publication_date 2023/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A non-trivial element of a group is a generalized torsion element if some products of its conjugates is the identity. The minimum number of such conjugates is called a generalized torsion order. We provide several restrictions for generalized torsion orders by using G-invariant norm and Alexander polynomials.

Related

• Generalized torsion elements in groups
• Generalized torsion elements in infinite groups
• Classification of generalized torsion elements of order two in 3-manifold groups
• Generalized torsion for knots with arbitrarily high genus
• Generalized torsion elements and hyperbolic links