Some Properties of normal subgroups determined from character tables

Abstract

Gcharacter tables of a finite group G were defined before. These tables can be very useful to obtain certain structural information of a normal subgroup from the character table of G. We analyze certain structural properties of normal subgroups which can be determined using their Gcharacter tables. For instance, we prove an extension of the Thompsons theorem from minimal Ginvariant characters of a normal subgroup. We also obtain a variation of Taketas theorem for hypercentral normal subgroups considering their minimal G-invariant characters. This generalization allows us to introduce a new class of nilpotent groups, the class of nMIgroups, whose members verify that its nilpotency class is bounded by the number of irreducible character degrees of the group.