SOLVABILITY OF A NORMAL SUBGROUP IN RELATION TO ITS CHARACTER DEGREES

Abstract

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 }

and

cd (^G/_N) = { (1) /   Irr (^G/_N)}