Ultrasolvable Covering of the Group Z2 by the Groups Z8, Z16, AND Q8

Abstract

Infinite series of nontrivial ultrasolvable embedding problems with cyclic kernel of order 8, 16, and quaternion kernel of order 8 are constructed. Among the embedding problems of a quadratic extension into a Galois algebra, 2-local nonsplit universally solvable problems with generalized quaternion or cyclic kernels are found. Bibliography: 14 titles.