The purpose of this paper is to prove the existence of a free subgroup of the group of all affine transformations on the plane with determinant 1 such that the action of the subgroup is locally commutative.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-1-3, author = {Kenzi Sat\^o}, title = {A locally commutative free group acting on the plane}, journal = {Fundamenta Mathematicae}, volume = {177}, year = {2003}, pages = {25-34}, zbl = {1055.20020}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-1-3} }
Kenzi Satô. A locally commutative free group acting on the plane. Fundamenta Mathematicae, Tome 177 (2003) pp. 25-34. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-1-3/