Monomial group
In mathematics, in the area of algebra studying the character theory of finite groups, an M-group or monomial group is a finite group whose complex irreducible characters are all monomial, that is, induced from characters of degree 1.
In this section only finite groups are considered. A monomial group is solvable by, presented in textbook in and. Every supersolvable group and every solvable A-group is a monomial group. Factor groups of monomial groups are monomial, but subgroups need not be, since every finite solvable group can be embedded in a monomial group, as shown by and in textbook form in.
The Symmetric group is an example of a monomial group which is neither supersolvable nor an A-group.
