On the Ultrasolvability of Some Classes of Minimal Nonsplit p-Extensions with Cyclic Kernel for p > 2

Abstract

For any nonsplit p > 2-extension of finite groups with a cyclic kernel and a quotient group with two generators all the accompanying extensions of which split, there exists a realization of the quotient group as a Galois group of number fields such that the corresponding embedding problem is ultrasolvable (i.e., this embedding problem is solvable and has only fields as solutions).