This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
A finite group is termed monomial (or sometimes, a M-group or -group) with respect to a field (whose characteristic does not divide the group order) if it satisfies the following equivalent conditions:
- Every irreducible representation of the group over is induced from a one-dimensional representation of a subgroup, i.e., a linear character.
- Every finite-dimensional linear representation of the group over is a monomial linear representation: it is a direct sum of representations induced from one-dimensional representations of subgroups.
Relation with other properties
- Elementary group
- Finite nilpotent group
- Finite supersolvable group: For full proof, refer: Finite supersolvable implies monomial