Yadchenko, A A

On Isaacs' problem

Let G be a π-soluble irreducible complex linear group of degree n such that a Hall π-subgroup H of it has odd order, is a TI-subgroup, and is not normal in G. In this paper it is established that n is divisible by |H| or by a power f>1 of some prime number such that f≡±1 (mod|H|). Bibliography: 15 titles.