A remark on a Theorem of J. G. Thompson
An important theorem by J. G. Thompson says that a finite group is -nilpotent if the prime divides all degrees (larger than 1) of irreducible characters of . Unlike many other cases, this theorem does not allow a similar statement for conjugacy classes. For we construct solvable groups of arbitrary -lenght, in which the lenght of any conjugacy class of non central elements is divisible by .