# Monomial implies solvable

(Redirected from Taketa theorem)
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.
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.