The solvability of monomial groups is a well-known result in character theory. Certain properties of Artin L-series suggest a generalization of these groups, namely to such groups where every irreducible character has some multiple which is induced from a character φ of U with solvable factor group U/ker(φ). Using the classification of finite simple groups, we prove that these groups are also s...

We study a class of finite groups, called almost monomial which generalize the groups and is connected with theory Artin L-functions. Our method research based on finding similarities whenever it possible.

An abundance of information regarding the structure of a finite group can be obtained by studying its irreducible characters. Of particular interest are monomial characters — those induced from a linear character of some subgroup — since Brauer has shown that any irreducible character of a group can be written as an integral linear combination of monomial characters. Our primary focus is the cl...

We give new evidence to the fact that structure of a solvable group can be controlled by irreducible monomial characters. In particular, we inspect role characters in Isaacs–Navarro–Wolf conjecture and Gluck’s conjecture.