Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Generalized torsion and decomposition of $3$–manifolds
HTML articles powered by AMS MathViewer

by Tetsuya Ito, Kimihiko Motegi and Masakazu Teragaito PDF
Proc. Amer. Math. Soc. 147 (2019), 4999-5008 Request permission

Abstract:

A nontrivial element in a group is a generalized torsion element if some nonempty finite product of its conjugates is the identity. We prove that any generalized torsion element in a free product of torsion-free groups is conjugate to a generalized torsion element in some factor group. This implies that the fundamental group of a compact orientable $3$–manifold $M$ has a generalized torsion element if and only if the fundamental group of some prime factor of $M$ has a generalized torsion element. On the other hand, we demonstrate that there are infinitely many toroidal $3$–manifolds whose fundamental group has a generalized torsion element, while the fundamental group of each decomposing piece has no such elements. Additionally, in the course of the proof of the first result, we give an upper bound for the stable commutator length of generalized torsion elements.
References
Similar Articles
Additional Information
  • Tetsuya Ito
  • Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
  • MR Author ID: 922393
  • ORCID: 0000-0001-8156-1341
  • Email: tetitoh@math.kyoto-u.ac.jp
  • Kimihiko Motegi
  • Affiliation: Department of Mathematics, Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156–8550, Japan
  • MR Author ID: 254668
  • Email: motegi.kimihiko@nihon-u.ac.jp
  • Masakazu Teragaito
  • Affiliation: Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-Hiroshima, 739–8524, Japan
  • MR Author ID: 264744
  • Email: teragai@hiroshima-u.ac.jp
  • Received by editor(s): November 26, 2018
  • Received by editor(s) in revised form: February 5, 2019
  • Published electronically: July 9, 2019
  • Additional Notes: The first named author was partially supported by JSPS KAKENHI Grants Number JP15K17540 and JP16H02145.
    The second named author was partially supported by JSPS KAKENHI Grant Number JP26400099 and Joint Research Grant of Institute of Natural Sciences at Nihon University for 2018.
    The third named author was partially supported by JSPS KAKENHI Grant Number JP16K05149.
  • Communicated by: David Futer
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4999-5008
  • MSC (2010): Primary 57M05, 20E06; Secondary 06F15, 20F60
  • DOI: https://doi.org/10.1090/proc/14581
  • MathSciNet review: 4011531