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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 00, Number 0, Xxxx XXXX, Pages 000{000
S 0002-9939(XX)0000-0
SHUFFLE THE PLANE
MIKL 
OS AB 
ERT AND TAM 
AS KELETI
Abstract. We prove that any permutation p of the plane can be obtained as
a composition of a xed number (209) of simple transformations of the form
(x; y) ! (x; y + f(x)) and (x; y) ! (x + g(y); y), where f and g are arbitrary
R ! R functions.
As a corollary we get that the full symmetric group acting on a set of
continuum cardinal is a product of nitely many (209) copies of two isomorphic
Abelian subgroups.
We investigate what transformations of the plane we can get by ( nitely many)
vertical and horizontal \slides", which we de ne as follows.
De nition 1. By a vertical (resp. horizontal) slide we mean an R 2 ! R 2 map of
the form (x; y) ! (x; y + f(x)) (resp. (x; y) ! (x + g(y); y)), where f (resp. g) is

  

Source: Abert, Miklos - Department of Mathematics, University of Chicago

 

Collections: Mathematics