Metacyclic 2-Extensions with Cyclic Kernel and Ultrasolvability Questions

Abstract

Necessary and sufficient conditions for a metacyclic extension to be 2-local and ultrasolvable are established. These conditions are used to prove the ultrasolvability of an arbitrary group extension which has a local ultrasolvable associated subextension of the second type. The obtained reductions enables us to derive ultrasolvability results for a wide class of nonsplit 2-extensions with cyclic kernel.