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On subgroups of the R. Thompson group F and other diagram groups -
Neue beitrage zur riemannischen funktionentheorie
- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/bdn060
- Publisher site
- See Article on Publisher Site
Abstract
This article discusses three families of groups: Z ≀ Zn, PL(In), and PL(Sn) (the last two being the families of groups of piecewise‐linear homeomorphisms of standard n‐dimensional spaces). It is shown that for positive n ∈ N, Z ≀ Zn embeds in PL(In), which embeds in PL(Sn). It is known that Z ≀ Z2 fails to embed in PL(I1), and this article extends that previous result to show that Z ≀ Z2 also fails to embed in PL(S1). The nature of the proofs of these embedding and non‐embedding results hints that there may be corresponding non‐embedding results in higher dimensions.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Oct 1, 2008