Free subgroups of SO_n(Q) and subgroups of SO_3(R) freely generate Z_2*Z_3

Conference in honor of Jan Mycielski (Colorado)

The first part is the proof of the existence of a free subgroup of the 5 by 5 special orthogonal group with rational entries whose action on the rational sphere with non-rational radius is without fixed points and whose action on the complete sphere is locally commtative. The second part shows partl