Vol. 5, Issue 9, Part C (2019)

Abstract
Our main aim is to derive the relationship between representation theory groups with invariants of subgroup of a finite group. We consider p-solvable groups for examining the converse cropped up due to Brauer's hypothesis. The converse of Brauer's hypothesis was proved partially for p-solvable groups by D. Gluck and T. Wolf. We show that for an arbitrary group for p-solvable groups, there exists some characteristics due to the heights of the characters in Irr (B) with respect to the exponents of the character of the group D (Dihedral group).