# Generalized torsion for hyperbolic $3$--manifold groups with arbitrary large rank

@inproceedings{Ito2021GeneralizedTF, title={Generalized torsion for hyperbolic \$3\$--manifold groups with arbitrary large rank}, author={Tetsuya Ito and Kimihiko Motegi and Masakazu Teragaito}, year={2021} }

Let G be a group and g a non-trivial element in G. If some nonempty finite product of conjugates of g equals to the trivial element, then g is called a generalized torsion element. To the best of our knowledge, we have no hyperbolic 3–manifold groups with generalized torsion elements whose rank is explicitly known to be greater than two. The aim of this short note is to demonstrate that for a given integer n > 1 there are infinitely many closed hyperbolic 3–manifolds Mn which enjoy the property…

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