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Generalized torsion orders and Alexander polynomials

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  08 January 2025

Tetsuya Ito Open the ORCID record for Tetsuya Ito [Opens in a new window]
Tetsuya Ito*
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
*
e-mail: tetitoh@math.kyoto-u.ac.jp
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Abstract

A nontrivial 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 the Alexander polynomial.

Keywords

Generalized torsion elementgeneralized torsion orderAlexander polynomialG-invariant norm

MSC classification

Primary: 20F60: Ordered groups 20F05: Generators, relations, and presentations 20F12: Commutator calculus

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 68 , Issue 2 , June 2025 , pp. 401 - 420
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

The author is partially supported by JSPS KAKENHI (Grant Nos. 19K03490, 21H04428, and 23K03110).

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