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- Title
Generation and simplicity in the airplane rearrangement group.
- Authors
Tarocchi, Matteo
- Abstract
We study the group TA of rearrangements of the airplane limit space introduced by Belk and Forrest (2019). We prove that TA is generated by a copy of Thompson's group F and a copy of Thompson's group T, hence it is finitely generated. Then we study the commutator subgroup [TA; TA], proving that the abelianization of TA is isomorphic to Z and that [TA; TA] is simple, finitely generated and acts 2-transitively on the so-called components of the airplane limit space. Moreover, we show that TA is contained in T and contains a natural copy of the basilica rearrangement group TB studied by Belk and Forrest (2015).
- Subjects
AIRPLANES; SIMPLICITY; COMMUTATION (Electricity)
- Publication
Groups, Geometry & Dynamics, 2024, Vol 18, Issue 2, p603
- ISSN
1661-7207
- Publication type
Article
- DOI
10.4171/GGD/772