Finite groups and their some special irreducible characters

In this thesis we worked with a new concept called strongly monolithic characters. Main result of this thesis can be listed as : • Finite groups with at most three strongly monolithic characters are solvable. • A non abelian finite group is nilpotent if and only if the division subgroups determined by the kernels of strongly monolithic characters are nilpotent. • The classification of finite groups whose nonlinear irreducible charatcers are all monolithic that has exactly one strongly monolithic character. • The classification of finite groups whose nonlinear irreducible charatcers are all monolithic that has exactly two strongly monolithic charatcers.