Complicated generalized torsion elements in Seifert fibered spaces with boundary

Himeno Keisuke

Journal of Knot Theory and Its Ramifications

In a group, a nontrivial element is called a generalized torsion element if some non-empty finite product of its conjugates is equal to the identity. There are various examples of torsion-free groups which contain generalized torsion elements. We can define the order of a generalized torsion element as the minimum number of its conjugates required to generate the identity. In previous works, three-manifold groups which contain a generalized torsion element of order two are determined. However, there are few previous studies that examine the order of a generalized torsion element bigger than two. In this paper, we focus on Seifert fibered spaces with boundary, including the torus knot exteriors, and construct concretely generalized torsion elements of order 3, 4, 6 and others in their fundamental groups.

Generalized torsion element

stable commutator length

eng

World Scientific Publishing

Electronic version of an article published as Journal of Knot Theory and Its Ramifications, 32, 12, 2050080(2023), https://doi.org/10.1142/S0218216523500803 © copyright World Scientific Publishing Company

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[DOI] https://doi.org/10.1142/S0218216523500803 isVersionOf