Abstract:
This thesis introduces the concepts of solvable and nilpotent groups
and presents important definitions like supersolvable groups, polycyclic
groups, Carter subgroups, metabelian groups ,hypercentral groups, HM=
groups, and Chernicov groups. This thesis includes applications in Galois
theory, and the solvability by radicals. Also, this research presents
examples, propositions, and applications related to solvable and nilpotent
groups.
Finally, this thesis presents three applications of solvable and
nilpotent groups, it discusses the solvability of Carter subgroups in the
groups in which every element is conjugate to its inverse, proofs of
interesting properties of metabelian groups, and this thesis study groups
with many hypercentral subgroups.
