Monomial group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

Symbol-free definition

A group is termed monomial (or sometimes, a M-group or $M_{1}$-group) if every irreducible representation of the group over the complex numbers is induced from a one-dimensional representation of a subgroup. Thus, any representation can, with a suitable choice of basis, be made into a representation with all the linear transformations being expressed by monomial matrices.

Relation with other properties

Stronger properties

• Finite nilpotent group
• Finite supersolvable group

Weaker properties

• Solvable group: This follows from the Taketa theorem