SOLVABILITY OF A NORMAL SUBGROUP IN RELATION TO ITS CHARACTER DEGREES

In this work, how the structure of a normal subgroup of a group G is influenced by the degrees of an appropriate subset of irreducible character of a group G was verified. The characters that were used in controlling the structure of N Δ G are exactly those whose kernels do not contain N.Given that N Δ G,Irr (G/N) = {Є Irr (G)/N  ker }andcd (G/N) = { (1) /   Irr (G/N)}Â