Monomial implies solvable

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This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property must also satisfy the second group property
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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.