Date of Award
2016
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
First Advisor
Richard M. Foote
Second Advisor
Byung S. Lee
Abstract
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 class of M-groups, those groups all of whose irreducible characters are monomial. A classical theorem of Taketa asserts that an M-group is necessarily solvable, and Dade proved that every solvable group can be embedded as a subgroup of an M-group. After discussing results related to M-groups, we will construct explicit families of solvable groups that cannot be embedded as subnormal subgroups of any M-group. We also discuss groups possessing a unique non-monomial irreducible character, and prove that such a group cannot be simple.
Language
en
Number of Pages
52 p.
Recommended Citation
McHugh, John, "Monomial Characters of Finite Groups" (2016). Graduate College Dissertations and Theses. 572.
https://scholarworks.uvm.edu/graddis/572