The Galois group of the tangency problem for plane curves.
A (monic) polynomial is called intersective if the congruence mod has a solution for all positive integers . Call nontrivially intersective if it is intersective and has no rational root. It was proved by the author that every finite noncyclic solvable group can be realized as the Galois group over of a nontrivially intersective polynomial (noncyclic is a necessary condition). Our first remark is the observation that the corresponding result for nonsolvable reduces to the ordinary...