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The planar 3-colorable subgroup ε of Thompson’s group F and its even part
Published online by Cambridge University Press: 25 November 2024
Abstract
We study the planar 3-colorablesubgroup 
$\mathcal{E}$ of Thompson’s group F and its even part 
${\mathcal{E}_{\rm EVEN}}$. The latter is obtained by cutting 
$\mathcal{E}$ with a finite index subgroup of F isomorphic to F, namely the rectangular subgroup 
$K_{(2,2)}$. We show that the even part 
${\mathcal{E}_{\rm EVEN}}$ of the planar 3-colorable subgroup admits a description in terms of stabilisers of suitable subsets of dyadic rationals. As a consequence 
${\mathcal{E}_{\rm EVEN}}$ is closed in the sense of Golan and Sapir. We then study three quasi-regular representations associated with 
${\mathcal{E}_{\rm EVEN}}$: two are shown to be irreducible and one to be reducible.
Keywords
MSC classification
Primary:
20F65: Geometric group theory
Information
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 68 , Issue 1 , February 2025 , pp. 173 - 197
- Copyright
- © The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.
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