METACYCLIC 2-EXTENSIONS WITH CYCLIC KERNEL AND ULTRASOLVABILITY QUESTIONS

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. Bibliography: 11 titles.
UDC 512.623.32 1. INTRODUCTION 1.1. The embedding problem associated with the exact sequence of finite groups [mathematical expression not reproducible], is to construct a Galois k-algebra L with the group [...]