Normal Subgroups of Odd Order Monomial P(a)q(b)-Groups

A finite group G is called monomial if every irreducible character of G is induced from a linear character of some subgroup of G. One of the main questions regarding monomial groups is whether or not a normal subgroup N of a monomial group G is itself monomial. In the case that G is a group of even order, it has been proved (Dade, van der Waall) that N need not be monomial. Here we show that, if G is a monomial group of order paq b, where p and q are distinct odd primes, then any normal subgroup N of G is also monomial.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Loukaki, Maria I.

Contributors dc:contributor

• Dade, Everett C.

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3023129

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86785