Abstract
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 [Formula: see text], [Formula: see text], [Formula: see text] and others in their fundamental groups.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.