ULTRASOLVABLE AND SYLOW EXTENSIONS WITH CYCLIC KERNEL

摘要

An extension of finite groups is said to be ultrasolvable if there exists a Galois extension of number fields such that its Galois group is a factor group of this group extension and all solutions of the corresponding embedding problem are fields. In the paper, necessary and sufficient conditions of the ultrasolvability of a group extension are obtained for extensions of odd order with cyclic kernel.