abstract. in this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

Let G be an arbitrary discrete group and let T = C[G] be its group algebra over the complex numbers C. If 9? is an irreducible representation of the algebra then 9i(r)=P is primitive and hence isomorphic to a dense set of linear transformations over D, the commuting ring of 9J [4, p. 28]. Let L be the center of D. If dimr, P < °o then we say that 9? is finite and since P is central simple over ...

A classical theorem on character degrees states that if a finite group has fewer than four degrees, then the is solvable. We prove corresponding result values by showing eight in its table, This confirms conjecture of T. Sakurai. also classify non-solvable groups with exactly values.