On a generalization of M-group
  In this paper, we will show that if for every nonlinear complex irreducible character of a finite group G, some multiple of it is induced from an irreducible character of some proper subgroup of G, then G is solvable. This is a generalization of Taketa's Theorem on the solvability of M-group. 
Tung Le, Jamshid Moori and Hung P. Tong-Viet
math.GR math.RT