Monomial implies solvable
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(Redirected from Taketa theorem)
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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Statement
If a finite group is a monomial group (sometimes referred to as an Mgroup or group), it is solvable. This result goes by the name of the Taketa theorem.
Related facts
Define a group to be a group all whose irreducible characters are induced from characters on subgroups of degree at most . Then, for , any finite group is solvable. groups are also termed almost solvable groups.