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

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- by Yoshifumi Matsuda and Shigenori Matsumoto PDF
- Proc. Amer. Math. Soc.
**149**(2021), 1-11 Request permission

## 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

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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
- 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
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 1-11 - MSC (2010): Primary 20F65; Secondary 20F05
- DOI: https://doi.org/10.1090/proc/15277
- MathSciNet review: 4172581