A free group acting without fixed points on the rational unit sphere
Free groups acting without fixed points on rational spheres
For every positive rational number q, we find a free group of rotations of rank 2 acting on (√q𝕊²) ∩ ℚ³ whose all elements distinct from the identity have no fixed point.
A locally commutative free group acting on the plane
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.
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