Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Invariable generation of certain groups of piecewise linear homeomorphisms of the interval


Authors: Yoshifumi Matsuda and Shigenori Matsumoto
Journal: Proc. Amer. Math. Soc. 149 (2021), 1-11
MSC (2010): Primary 20F65; Secondary 20F05
DOI: https://doi.org/10.1090/proc/15277
Published electronically: October 9, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ P$ be the group of all the orientation preserving piecewise linear homeomorphisms of the interval $ [0,1]$. Given any $ a>1$, let $ P^a$ be the subgroup of $ P$ consisting of all the elements with slopes in $ a^\mathbb{Z}$, and let $ P^\mathbb{Q}$ be the subgroup of $ P$ consisting of all the elements with slopes and breaks in $ \mathbb{Q}$. We show that the groups $ P$, $ P^a$, $ P^\mathbb{Q}$, as well as Thompson group $ F$, are invariably generated.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 20F65, 20F05

Retrieve articles in all journals with MSC (2010): 20F65, 20F05


Additional Information

Yoshifumi Matsuda
Affiliation: Department of Physics and Mathematics, College of Science and Engineering, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara-shi, Kanagawa, 252-5258 Japan
Email: ymatsuda@gem.aoyama.ac.jp

Shigenori Matsumoto
Affiliation: Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda-Surugadai, Chiyoda-ku, Tokyo, 101-8308 Japan
Email: matsumo@math.cst.nihon-u.ac.jp

DOI: https://doi.org/10.1090/proc/15277
Keywords: Invariable generation, piecewise linear homeomorphism, Thompson group
Received by editor(s): August 18, 2018
Received by editor(s) in revised form: September 4, 2018, September 20, 2019, and March 11, 2020
Published electronically: October 9, 2020
Additional Notes: The first author was partially supported by Grant-in-Aid for Scientific Research (C) No. 17K05260.
The second author was partially supported by Grant-in-Aid for Scientific Research (C) No. 18K03312.
Communicated by: Kenneth Bromberg
Article copyright: © Copyright 2020 American Mathematical Society