 
Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 00, Number 0, Xxxx XXXX, Pages 000{000
S 00029939(XX)00000
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 dene as follows.
Denition 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
