We prove that every permutation of ω² is a composition of a finite number of axial permutations, where each axial permutation moves only a finite number of elements on each axis.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-2-7, author = {Pawe\l\ Klinga}, title = {Axial permutations of $\omega$$^2$}, journal = {Colloquium Mathematicae}, volume = {144}, year = {2016}, pages = {267-273}, zbl = {1331.03033}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-2-7} }
Paweł Klinga. Axial permutations of ω². Colloquium Mathematicae, Tome 144 (2016) pp. 267-273. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-2-7/