Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Shuffle the plane


Authors: Miklós Abért and Tamás Keleti
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
Published electronically: September 19, 2001
MathSciNet review: 1862136
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. M. Abért, Symmetric groups as products of Abelian subgroups, to appear in Bull. London Math. Soc.
  • 2. O. Ore, Some remarks on commutators, Proc. Amer. Math. Soc. 2 (1951), 307-314. MR 12:671e
  • 3. P. Komjáth, Five degrees of separation, to appear in Proc. Amer. Math. Soc.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 26B40, 03E05, 20B30, 20D40

Retrieve articles in all journals with MSC (2000): 26B40, 03E05, 20B30, 20D40


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
Email: elek@cs.elte.hu

DOI: https://doi.org/10.1090/S0002-9939-01-06344-4
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
Article copyright: © Copyright 2001 American Mathematical Society