Galois extensions with bounded ramification in characteristicp on a question of S. Abhyankar

Abstract

Given an arbitrary congruence function fieldK of characteristicp and a finite groupG with a uniquep-Sylow subgroupp(G) which is abelian and for which the factor groupG/p(G) is nilpotent and hass generators, there exists a geometric Galois extensionL/K with Galois groupG in which preciselys prime divisors ofK are ramified.