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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
MathSciNet review: 4172581
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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.


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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
MR Author ID: 878267
ORCID: 0000-0001-9092-4255
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
MR Author ID: 214791
ORCID: 0000-0002-5851-7235
Email: matsumo@math.cst.nihon-u.ac.jp

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