Monomial implies solvable

Statement
If a finite group is a monomial group (sometimes referred to as an M-group or $$M_1$$-group), it is solvable. This result goes by the name of the Taketa theorem.

Related facts
Define a $$M_k$$-group to be a group all whose irreducible characters are induced from characters on subgroups of degree at most $$k$$. Then, for $$k \le 3$$, any finite $$M_k$$-group is solvable. $$M_4$$-groups are also termed almost solvable groups.