Shuffle the plane
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- by Miklós Abért and Tamás Keleti PDF
- Proc. Amer. Math. Soc. 130 (2002), 549-553 Request permission
Abstract:
We prove that any permutation $p$ of the plane can be obtained as a composition of a fixed number (209) of simple transformations of the form $(x,y)\to (x,y+f(x))$ and $(x,y)\to (x+g(y),y)$, where $f$ and $g$ are arbitrary $\mathbb {R}\to \mathbb {R}$ functions. As a corollary we get that the full symmetric group acting on a set of continuum cardinal is a product of finitely many (209) copies of two isomorphic Abelian subgroups.References
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Additional Information
- Miklós Abért
- Affiliation: Department of Algebra, Eötvös Loránd University, Kecskeméti u. 10-12, 1053 Budapest, Hungary
- Email: abert@cs.elte.hu
- Tamás Keleti
- Affiliation: Department of Analysis, Eötvös Loránd University, Kecskeméti u. 10-12, 1053 Budapest, Hungary
- MR Author ID: 288479
- Email: elek@cs.elte.hu
- Received by editor(s): July 11, 2000
- Published electronically: September 19, 2001
- Additional Notes: The research of the first author was supported by the Hungarian National Foundation for Scientific Research Grant 32325
The research of the second author was supported by the Hungarian National Foundation for Scientific Research Grant T26176 - Communicated by: David Preiss
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 549-553
- MSC (2000): Primary 26B40; Secondary 03E05, 20B30, 20D40
- DOI: https://doi.org/10.1090/S0002-9939-01-06344-4
- MathSciNet review: 1862136