On Representation of Monomial Groups - Bedaiwi, S A; Hajim, A A (Al-Nahrain Journal of Science, 2011)
Taketa shows that all monomial groups (commonly written as M-groups) are solvable. Gajendragadkar gives the notion of π-factorable character. We show that an irreducible character of an M-group is primitive if it is π-factorable. Issacs proves that product of two monomial characters is a monomial. We extend this fact to include any finite number of monomial characters consequently we prove that any product of finite number of M-groups is an M-group. We show that any group of order 45 is an M-group and for any group G, the factor group is an M-group.