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.

In the 1970s, Isaacs conjectured that there should be a logarithmic bound for the length of solvability of a p-group G with respect to the number of different irreducible character degrees of G. So far, there are just a few partial results for this conjecture. In this note, we say that a pro-p group G has property (I) if there is a real number D = D(G) that just depends on G such that for any o...